OIS Interest Rate and LIBOR-OIS Spread?

What is OIS Rate? 

OIS is an American Rate that is currently being pushed by NY Fed a lot in American markets after the recent global financial crisis. 

This is an interest rate that banks charge each other for an overnight lending to each other. Counterpart to this rate for interbank lending is called LIBOR, which I mentioned in my previous post. 

OIS rate when compared with corresponding LIBOR, is always lower. The rationale is a lending for just an overnight is much more safer than lending to a bank for a longer period say 3M or 1Yr. Since OIS matures overnight, there is a very little risk for counterparty default. This rate is heavily being used primarily in Derivatives instruments where collaterals are being posted by counterparties. 

What is LIBOR-OIS Spread? 

A spread is usually defined as a gap between two attributes such as Gap between two prices or Gap between two interest rates. 

A LIBOR-OIS spread is the gap between LIBOR rate and Overnight Indexed Swap rate. One can imagine that LIBOR will be more riskier than OIS due to longer tenors in LIBOR. The gap can be anywhere between 10-40 bps (1 basis point is 1% of 1%, 100 bp = 1%). In financial market, this gap is closely being monitored for 2 reasons: 

1. If Market sees that banks are still credible but gap is widening then it offers a great arbitrage opportunity for bankers. They can borrow in OIS and Lend in LIBOR.

2. If scenario 1 is not true then it simply means that Financial market is getting into trouble and banks dont feel comfortable in leading to each other for longer periods. 

During financial crisis of 2008, LIBOR - OIS spread jumped from 10-15 basis points to 350 basis points range. Hence, the spread between LIBOR-OIS can be seen as the price of banking risk. 

Hope this helps.

Nitin

LIBOR Interest Rate

What is LIBOR?

In this post I would like to discuss a very important interest rate from UK, LIBOR, that banks in UK use as a Benchmark.

LIBOR - London Interbank Offering Rate

LIBOR is the most important interest rate that is used in LONDON. It is the borrowing rate that banks charge each other for lending various currencies. The rate is published by BBA where the top 16 banks release their rates for charging to other banks and BBA publishes one rate after using some formula behind it.  LIBOR is then used as a benchmark and all financial instruments that require interest rate as a part, would use LIBOR as a benchmark and add some spread based on the credibility. 

In a simple way, consumers will need to pay an interest rate higher than the LIBOR because no one can borrow at LIBOR except the banks themselves. 

These borrowing and lending can happen in any currency such as USD, Euro, Pound and so on. Hence, there is a corresponding LIBOR for USD, EURO, Pound or other currencies. Other than currency, the next important attribute of the LIBOR is the tenor, the duration for which banks want to lend another bank or so. 

Hence, there would be a LIBOR USD rate for 1M, 3M, 6M, 1Y and similarly LIBOR Sterling rate for the same tenor points.

Usage: 

These rates are used as a benchmark to offer various financial instruments to consumers such as Mortgage Rate, Auto Loan Rate, Student Loan and so on and so forth.

Process is very Simple: 

Scenario 01 

Let's say Bank A's can borrow at Libor from Bank B 

Bank A has a customer C1 who wants a short term loan for 1 Yr

Bank A sees the customer C1 to be of less risky and happy to give loan at 0.5% Margin

Finally, Bank will charge Customer C1 an interest rate of Libor + 0.5% + Whatever Processing Fee 

Scenario 02 

Let's say Bank A's can borrow at Libor from Bank B 

Bank A has a customer C2 who wants a short term loan for 1 Yr

Bank A sees the customer C2 to be of more riskier than C1 BUT happy to give loan at 2% Margin

Finally, Bank will charge Customer C1 an interest rate of Libor + 2% + Whatever Processing Fee 

Same process can go for a borrowing in any other currency such as Euro, Sterling and so on. 

Hope this helps,

Nitin

Security Markets Wisdom (Part 4)

Finally, to wrap it all up, I am putting together the thoughts by 2 market leaders, Dennis Gartman and James Montier. 

Again, no matter how many times it has been stressed out that market forces will bring all greed and fear into the equilibrium state as no one can keep on making money all the times. One can think of every state of the market is an equilibrium state for the past and a start of new disequilibrium for future movements. Let me explain it further - Equilibrium from past means that supply and demand would have brought the equilibrium to the price dimension where people would have taken their profits or losses out. Hence, some people would have moved out of the markets due to portfolio ruin and some would have made good profits with their bets. Now to replace the losers, new participants come in and join the market. With new participants, a new combination of greed and fear comes into the play. With new hunger for risk and reward again a disequilibrium will be created causing people to be away from risk adjusted forces. Again, greed and fear will come back in and the same process will keep on going in cycles. 

I am extremely sorry as this final post is going to be a little lengthy so I ask for your patience to scroll until the bottom so that you can fully appreciate the wisdom put forth by these pundits for people such as us. 

Dennis Gartman's Wisdom on Trading Securities

1. Never, under any circumstance add to a losing position.... ever! Nothing more need be said; to do otherwise will eventually and absolutely lead to ruin!

2. Trade like a mercenary guerrilla. We must fight on the winning side and be willing to change sides readily when one side has gained the upper hand.

3. Capital comes in two varieties: Mental and that which is in your pocket or account. Of the two types of capital, the mental is the more important and expensive of the two. Holding to losing positions costs measurable sums of actual capital, but it costs immeasurable sums of mental capital.

4. The objective is not to buy low and sell high, but to buy high and to sell higher. We can never know what price is "low." Nor can we know what price is "high." Always remember that sugar once fell from $1.25/lb to 2 cent/lb and seemed "cheap" many times along the way.

5. In bull markets we can only be long or neutral, and in bear markets we can only be short or neutral. That may seem self-evident; it is not, and it is a lesson learned too late by far too many.

6. "Markets can remain illogical longer than you or I can remain solvent," according to our good friend, Dr. A. Gary Shilling. Don't try to find logic in market movements all the times. 

7. Sell markets that show the greatest weakness, and buy those that show the greatest strength. Metaphorically, when bearish, throw your rocks into the wettest paper sack, for they break most readily. In bull markets, we need to ride upon the strongest winds... they shall carry us higher than shall lesser ones.

8. Try to trade the first day of a gap, for gaps usually indicate violent new action. We have come to respect "gaps" in our nearly thirty years of watching markets; when they happen (especially in stocks) they are usually very important.

9. Trading runs in cycles: some good; most bad. Trade large and aggressively when trading well; trade small and modestly when trading poorly. In "good times," even errors are profitable; in "bad times" even the most well researched trades go awry. This is the nature of trading; accept it.

10. To trade successfully, think like a fundamentalist; trade like a technician. It is imperative that we understand the fundamentals driving a trade, but also that we understand the market's technicals. When we do, then, and only then, can we or should we, trade.

11. Respect "outside reversals" after extended bull or bear runs. Reversal days on the charts signal the final exhaustion of the bullish or bearish forces that drove the market previously. Respect them, and respect even more "weekly" and "monthly," reversals.

12. Keep your technical systems simple. Complicated systems breed confusion; simplicity breeds elegance.

13. Respect and embrace the very normal 50-62% retracements that take prices back to major trends. If a trade is missed, wait patiently for the market to retrace. Far more often than not, retracements happen... just as we are about to give up hope that they shall not.

14. An understanding of mass psychology is often more important than an understanding of economics. Markets are driven by human beings making human errors and also making super-human insights.

15. Establish initial positions on strength in bull markets and on weakness in bear markets. The first "addition" should also be added on strength as the market shows the trend to be working. Henceforth, subsequent additions are to be added on retracements.

16. Bear markets are more violent than are bull markets and so also are their retracements.

17. Be patient with winning trades; be enormously impatient with losing trades. Remember it is quite possible to make large sums trading/investing if we are "right" only 30% of the time, as long as our losses are small and our profits are large.

18. The market is the sum total of the wisdom ... and the ignorance...of all of those who deal in it; and we dare not argue with the market's wisdom. If we learn nothing more than this we've learned much indeed.

19. Do more of that which is working and less of that which is not: If a market is strong, buy more; if a market is weak, sell more. New highs are to be bought; new lows sold.

20. The hard trade is the right trade: If it is easy to sell, don't; and if it is easy to buy, don't. Do the trade that is hard to do and that which the crowd finds objectionable. Peter Steidelmeyer taught us this twenty five years ago and it holds truer now than then.

21. There is never one cockroach! This is the "winning" new rule submitted by our friend, Tom Powell.

22. All rules are meant to be broken: The trick is knowing when... and how infrequently this rule may be invoked!

Finally, few last ones by James Montier

James Montier's 7 Immutable Laws Of Investing

1. Always insist on a margin of safety

2. "This time is different" is actually never different

3. Be patient and wait for the fat pitch

4. Be contrarian

5. Risk is the permanent loss of capital, never a number

6. "Be leery of leverage". Leverage has been the single most cause of most of the failures of almost all types of trades be it institutional or retailer.

7. Never invest in something you don't understand

I truly hope that this series was a good read to all my dear readers. I am happy to hear your comments, feedback or anything you would like to share. 

-Nitin

Security Markets Wisdom (Part 3)

I hope you have truly enjoyed reading the first 2 parts of the Market Wisdom series. Here, in the part 3, I will talk about Gerlad Loeb and in the final post of the series, Part 4, couple of more guru's sharing to wrap it up.

Gerald Loeb's Wisdom:

1. The most important single factor in shaping security markets is public psychology.
2. To make money in the stock market you either have to be ahead of the crowd or very sure they are going in the same direction for some time to come.
3. Accepting losses is the most important single investment device to insure safety of capital.
4. The difference between the investor who year in and year out procures for himself a final net profit, and the one who is usually in the red, is not entirely a question of superior selection of stocks or superior timing. Rather, it is also a case of knowing how to capitalize successes and curtail failures.
5. One useful fact to remember is that the most important indications are made in the early stages of a broad market move. Nine out of ten times, the leaders of an advance are the stocks that make new highs ahead of the averages.
6. There is a saying, "A picture is worth a thousand words." One might paraphrase this by saying a profit is worth more than endless alibis or explanations. . . prices and trends are really the best and simplest "indicators" you can find.
7. Profits can be made safely only when the opportunity is available and not just because they happen to be desired or needed.
8. Willingness and ability to hold funds "non-invested" while awaiting real opportunities is a key to success in the battle for investment survival.
9. In addition to many other contributing factors of inflation or deflation, a very great factor is the psychological. The fact that people think prices are going to advance or decline very much contributes to their movement, and the very momentum of the trend itself tends to perpetuate itself.
10. Most people, especially investors, try to get a certain percentage return, and actually secure a minus yield when properly calculated over the years. Speculators risk less and have a better chance of getting something, in my opinion.
11. I feel all relevant factors, important and otherwise, are registered in the market's behaviour, and, in addition, the action of the market itself can be expected under most circumstances to stimulate buying or selling in a manner consistent enough to allow reasonably accurate forecasting of news in advance of its actual occurrence.
12. You don't need analysts in a bull market, and you don't want them in a bear market

-Nitin

Security Markets Wisdom (Part 2)

I hope you all liked Part 1 of Market Wisdom by Jesse. In Part 2, I will share the facts by another pundit, Bernard Baruch. You would notice, though these people are different, yet they are trying to teach us all the same thing. Discipline and Do not speculate. 

Wisdom by Bernard Baruch-

1. Don't speculate unless you can make it a full-time job.

2. Beware of barbers, beauticians, waiters, taxi drivers — of anyone — bringing gifts of "inside" information or "tips."

3. Before you buy a security, find out everything you can about the company, its management and competitors, its earnings and possibilities for growth.

4. Don't try to buy at the bottom and sell at the top. This can't be done — except by liars. [This is an important fact that bottoms and tops just can't be traded. No one knows about it when they occur. People only know it after the fact and then they would claim how they spotted it. Those who claim to have it spotted very well, must show a history of it to have the skills acknowledged. Else, it was just a pure luck and one shouldn't trade on luck]

5. Learn how to take your losses quickly and cleanly. Don't expect to be right all the time. If you have made a mistake, cut your losses as quickly as possible.

6. Don't buy too many different securities. Better have only a few investments which can be watched.

7. Make a periodic reappraisal of all your investments to see whether changing developments have altered their prospects.

8. Study your tax position to know when you can sell to greatest advantage.

9. Always keep a good part of your capital in a cash reserve. Never invest all your funds.

10. Don't try to be a jack of all investments. Stick to the field you know best.

Hope you enjoy it.

Nitin

Security Markets Wisdom (Part 1)

Market Wisdom - In this series I will talk about most of the trading rules that have been shared by market pandits from the past and yet they are been violated in today's world by traders in the hopes of seeing a different outcome.

Trading Securities in markets are primarily driven by two psychological biases - Greed and Fear. Greed lets people take risks that they haven't thought through deep enough and they only appreciate it after seeing it. These excessing greed can lead to either huge drawdowns or entire portfolio ruin.

There have been many market pundits who have shared their wisdom from their own experiences. In this series of "Market Wisdom", I will share what they told us and yet people lack discipline and violate these rules over and over leading to negative returns in Portfolio.

In Post 1 of the series, I will post the infamous "Jesse Livermore's" trading rules that were written back in 1940. All of these rules are taken either from reading books on JL, or through various readings at reliable financial resources websites.

Market Wisdom by Jesse Livermore: 

1. Nothing new ever occurs in the business of speculating or investing in securities and commodities.
2. Money cannot consistently be made trading every day or every week during the year.
3. I become a buyer as soon as a stock makes a new high on its movement after having had a normal reaction.
4. Never buy a stock because it has had a big decline from its previous high.
5. Never sell a stock because it seems high-priced.
6. Markets are never wrong – opinions often are.
7. If you cannot make money out of the leading active issues, you are not going to make money out of the stock market as a whole.
8. The real money made in speculating has been in commitments showing in profit right from the start.
9. As long as a stock is acting right, and the market is right, do not be in a hurry to take profits.
10. One should never permit speculative ventures to run into investments.
11. The money lost by speculation alone is small compared with the gigantic sums lost by so-called investors who have let their investments ride.
12. Never average losses.
13. Wishful thinking must be banished.
14. Big movements take time to develop.
15. Do not become completely bearish or bullish on the whole market because one stock in some particular group has plainly reversed its course from the general trend.
16. It is much easier to watch a few than many. [Don't trade too many different securities]
17. Only a handful of people ever make money on tips. Beware of inside information. If there was easy money lying around, no one would be forcing it into your pocket.
18. The human side of every person is the greatest enemy of the average investor or speculator.
19. It is not good to be too curious about all the reasons behind price movements.
20. The leaders of today may not be the leaders of two years from now. 
21. Don't trust your own opinion and back your judgment until the action of the market itself confirms your opinion.

This is the end of Part 1. Stay tuned for Part 2

-Nitin

Probability Basics and Expected Value

Probability is defined as a chance that a random number will have a particular outcome. For example, there is a 50-50 chance (hence 50% probability) that a fair coin will have a heads land up. If you gather all the possible outcomes of a random variable, such as the outcomes of the dice when it is rolled up, it generates a distribution which is the key in Probability space as it gives an insight of all possible values of the Random Variable.

What is a Random Variable: 
Random variable is just a name that can be anything where an analysis needs to be performed. Common examples are, outcome of a toss coin, outcome of a Dice roll, Daily returns of the financial instrument and so on. Once you know the outcomes of the Random variable, you can assign the probabilities attached to it to generate Probability Distribution. It is this probability distribution that helps to forecast future outcomes with certain confidence.

There are 4 main topics that one must consider while working with Probability.
1. CDF - Cumulative Distribution Function - CDF, F(.), of a random variable, X, is defined as:
                F(x) := P(X <= x)
                (Probability of X is less than or equal to x)

2. PMF - Probability Mass Function. p(.) is a Probability Mass function for the random variable, X,
                P(X in A) = Summation (p(x)) for all x in A

3. Expected Value: Expected value of a random variable, X, is given by the sigma of probability weights of the random variable.
                E(X) := Summation (Random value * Probability of Random Value)

4. Variance: Variance of a Random variable, X, is defined as
                Var(X) := E[(X - E[X]^2)]
                             = E[X^2] - E[X]^2
Variance is also known as Mean of the Squares - Square of the Mean.

Real World Application: 
What is the expected value of a fair dice roll?
As we know a fair dice will have 6 faces, numbered from 1 through 6 with each face with equal probability of 0.1667 or 16% chance of each number showing up.

Expected value then becomes:
0.1667 *(1) + 0.1667 *(2) + 0.1667 *(3) + 0.1667 *(4) + 0.1667 *(5) + 0.1667 *(6) = 3.5

Therefore one can say that the average value of a dice outcome is 3.5 or there is a 50-50 chance of beating the average value in which case 50% of the times, a dice can have a value higher than Expected value (4,5,6) or 50% chance that it can have lower than expected values of 3.5 (1,2,3).

Simple stuff - isn't it?

Nitin

High Frequency Trading Overview

High Frequency Trading Overview: 

In this post, I would like to talk about a little bit about High Frequency Trading, some of the key players around it and so on.

So what is HFT and how is it different than Traditional Trading? 
High Frequency Trading refers to fast allocation/re-allocation or turnover of trading capital. In Traditional trading, a trader will look at some of the components of the trading strategy such as Charts with indicators (moving averages, RSI etc...) before committing capital to the trade. On the other hand, in HFT, computers make the decisions to fire the trade based on some econometric model that is fully tested out (back-tested) by the trader. In HFT, trade execution speed is the key as the trades might be executed in a fraction of seconds/milliseconds/nanoseconds and traditional traders can't operate at such a low latency.

* In HFT, Low latency refers to the speed of executing an order. A low latency can be a trading strategy in its own right when the high speed of execution can be used an arbitrage strategy where there are price difference found on the same security on multiple exchanges for the same security.

There are 4 key characteristics of HFT:
1. Tick by Tick Data Processing
2. High Capital Turnover (HCT)
3. Intraday Entry and Exit
4. Algorithmic Trading

Some of the key players in HFT are: DE Shaw, Renaissance Technologies, and Towa Research Capital

3 Major components of HFT system are:
1. Highly Quantitative, Econometric models that forecast short term price moves based on contemporary market conditions
2. Advanced Computer systems built to quickly execute the complex econometric model
3. Capital applied and monitored with in Risk Management and Cost Management framework

In practice, an HFT firm will use 2 years of tick level data to backtest a strategy before committing live capital on it. Since setting up an HFT strategy requires pretty sophisticated level of understanding in Finance and Economics, most of the staffing at such firms are Ph.D in Quantitative Research (Finance/Economics/Physics)

Finally, an HFT operation is more likely to survive & proper if it had leverage and high Sharpe Ratios. Leverage helps to cover the operational costs and Sharpe Ratio helps in reducingthe risk of catastrophic losses and fund ruin.

Please feel free to comment should you have further questions related HFT.

-Nitin

What is Basel III

What is Basel III 

Basel Accord is a set of banking regulations & standards designed to maintain the integrity of financial system. The original set of standards were called Basel I, followed by II, and III. Basel III is a crucial regulatory response to financial crisis and a major step forward towards a stronger and stable banking system. These standards are developed by Basel committee in Switzerland and then each country copies the framework and applies into domestic financial sector. Basel III is a successor of Basel II and hence more rigid with its requirement so as to keep healthy financial system globally.

Basel III focuses on Capital adequacy requirements to have a more resilient banking system such that during stress times banks have enough liquidity to keep a fully functional banking system without government intervention. Also one of the goals of the Accord is to substantially lower the cost of economic loss given shocks in the economy.

Before we go any further on it, one must understand the functioning model of banking system. Banks have usually deposits as cash which we all deposit as a part of our salary, trading account or whatever else. Banks usually need to reinvest the capital it collected back into capital markets to generate more money. Banks usually use this capital to give out loans to consumers, bankers checks, short term loans to corporations or they even themselves go ahead and buy some assets such as US Treasury or Euro denominated bonds, Gold  etc...

During crisis, banks usually go through difficult circumstances such as :
1. Asset values might start to go down faster than banks original predicted. These assets might lose 20-30% in their value within weeks or so.
2. Depositors might start drawing cash faster than bankers originally anticipated.

If these situations continue for a prolonged period, banks might themselves run into liquidity crisis where they don't have any more cash left to give back to depositors or any sort of money to lend out. So, their assets on  the balancesheet are losing value and their cash deposits are depleting faster than anticipated. Under these circumstances, banks will run out to Central Government for protection. Governments also have to go through difficult choices at this time. Government usually have following 2 choices only:

1. They can let the financial institution fail and hence cripple the financial markets further. OR
2. Rescue them and hence adversing the moral hazard. (This one is really tricky as commercial banks have the benefit of taking risky bets knowing the central governments can bail them out while the end consumer might not receive any benefit from it. During good times banks can make money off the consumers and during bad times banks can make money off governments so they are in win-win situation)

So, now what Basel III Accord truly wants is to restrict banks from being too dependent on government bailout and hence making regulations for better functioning financial system.

4 Keys areas of Basel III regulations are:

1. Risk Management & Corporate Governance: During Financial crisis of 2008 till today, it was observed while Risk Management and Corp Governance policies were implemented across banking sector, they were pretty weak. Lack of governance influenced risky bets and hence the crisis. Basel III looks into this issue and make recommendation for improvement.

2. Better and More Capital: Basel III looks for better Quality and Quantity of Capital Requirement. The accord requires 7% of Risk Weighted Capital must be common equity with highly liquid assets. In Basel II, the requirement was only a mere 2%.

3. Systemic Risk: Systemic Risk is defined as the event in which the failure of few banking institutions can lead the financial system collapse and hence a system failure. Basel III looks into this issue and tries to provide solutions in at least 2 dimensions (Time and Cross Sectional)

4. Liquidity Management: Before financial crisis of 2008, all banks were taking a free ride on liquidity. It was treated as a free good with the impression that everyone will have access to it. However, after the crisis, it was no longer a free good. Central Governments across the globe (FED, BOE, ECB, RBA etc...) have to pump in liquidity to have money markets fully functioning. This is the first time when global liquidity rules are defined to ensure that there will be enough liquidity under stress times available in the banking sector to keep them functioning.

This is all for Basel III

-Nitin

Symptoms to Worry about Personal Finances!!

When to worry about your personal finances? 

While this observation started with noticing American behavior, the symptoms described below can be hold universally true regardless of the location. It's people's habits that puts them into financial trouble and not the location but American are used to exploit it to the extreme end of the spectrum.

Americans are known to live beyond their means. American Consumer Debt, US Govt Debt, and everything around Debt have sky-rocket records around Americans. Most of the Americans would look for path of least resistance to earn the extra dollar that they need. They rather buy Lottery, which is poor man's tax, than doing actual work which will make them millionaire. Statistics have shown that you have a better chance of getting hit by a lightning storm than winning a lottery yet people are willing to do the same thing over and over and expecting a different result each time. It's sad but the truth is most of the American Wealth is highly skewed to the right where few people own most of it and others barely put food to the table.

Following framework might show symptoms when to worry about your personal finances:
1. Your income is not increasing (or perhaps decreasing) but you are still spending too much money on credit cards. A simple outstanding balance of "Month Over Month", MoM, will paint the picture clearly.
2. You are doing credit card balance transfers too many times. With each Balance Transfer, credit card companies charge a one time processing fee. So, you already paid more money in Bank's pocket than keeping in yours.
3. You are applying for new credit cards all the times since you maxed out on your existing ones
4. You are missing payments on your credit cards or paying the minimum payment most of the times
5. You are using credit cards for every little purchase such as Gasoline or even to pay your rents
6. You are using credit cards with merchants even when they charge a convenience fee of 2.5 - 5%
7. You have converted your Amortized Mortgage to an Interest Only Mortgage to lower down your payment schedule
8. You do not have an accurate picture of how much debts you truly have (Exclude Primary Mortgage)
9. You might have borrowed money from your 401K or IRA or any other Retirement Fund
10. You have taken money from your family or friends that you are not ready to return yet

This framework gives some guidelines when people are already into the trouble or very soon will be entering into it if appropriate actions are not taken.

How to avoid these pitfalls or manage finance better? 
Money management is an art than science. Most of it comes with a discipline and strong adherence to the rules that money management brings. If you don't follow it or try to find back-door to escape from it, you will get into financial catastrophe.

Following framework might help you to manage your finance better:
1. If you can't pay your credit card balance completely with your monthly statement, don't use it. You should start getting into the habit of using ATM cards aka Debit Cards than credit cards. Since Debit cards debit your account right away, you will have a much clear picture of your savings. Don't get caught up by those Air miles on credit card if you can't make full payment on credit card by End of Month.
2. Check your Bank Account on daily basis or at least every other day to ensure that you don't have any surprised bank fees. If you see so, call bank immediately and ask for a one time waiver. Make sure you understand why such costs were there so you don't get into the same situation
3. Stop Spending money on things that are not needed until your credit cards are paid off. I know you would have to convince your wife to stop spending but it's worth it. In the long run, a wife with a debt free husband will be much happier than indebted husband. So, be ready for the fights but convince her that this is the right thing to do.
4. Pay the credit cards that have the least balance first. And, just follow the same protocol until you have paid off everything
5. Be proactive to make your payments. Set up alerts or automatic withdraw from your checking account. Don't make payments on the last day and pay convenience fee to the merchant. These are just scams.
6. Stop carrying too many credit cards in your pocket. In fact, don't ever bother to carry more than one. It's OK to not use them. It won't bring down your status in society
7. You must Save. You can open up a Systematic investment Plan with a broker or your own bank. Look more into it based on your preference.
8. Try to eliminate anything and everything where you are paying interests. If it means no discretionary spending for next 2 years, so be it.

That's all I can say about it. Please feel free to comment or any feedback you would like to share.

-Nitin

Portfolio With Options - Greeks Sensitivity

Portfolio With Options - Greeks Sensitivity

Put-Call Parity can be chosen as a primary tool for measuring portfolio risk. Not only it can help one to determine portfolio risk, but also to exploit Arbitrage in case it exists when Put-Call Parity equation is violated.

Put-Call Parity in a nutshell is defined as:

Put(K) + Stock - Call(K) = Riskfree Bond ---------------------------(1) 

Equation (1) is the heart of the option portfolio so it must be respected at all times. You can think of this equation as a Portfolio Replication such that their market price must match. In case the market prices do not match on both sides of the equation, the arbitrageur can sell the overvalued portfolio and can buy the undervalued portfolio and keep them on books until maturity and collect the risk free cash.

Also, the above scenario assumes that the options are European Style and their maturity is the same as the maturity of the risk free bond, and no dividends will be offered. The result of the above portfolio is to generate the Riskless Cash flow equal to the Strike of the option at expiration.

Let me explain why would it work:
Scenario 1 - Stock Price > Strike Price
Here the short call will be exercised, put will expire worthless, and you WILL BE FORCED to sell the stock at Strike Price

Scenario 2 - Stock Price < Strike Price
Here the short call will expire worthless, put will be exercised, and you WILL sell the stock at Strike Price

Scenario 3 - Stock Price = Strike Price
Here both options will expire worthless and stock will be sold for Strike price which should be same as market price at that moment

So, it must be clear the total payoff in all scenarios will the same amount, the strike price K. Only a  Riskfree bond with a maturity value of K can give the same payoff as every other bond will carry risk and your final payoff can be substantially different than K based on other risk factors.

Such portfolios are called Riskless Portfolios, Market Neutral Portfolios, Delta Neutral Portfolio, Riskless Hedged Portfolios and so on. They all mean same thing though that there is no risk if either of these  portfolios are held until maturity.

Below table shows a little bit of Options Greeks math to convey the same result that total exposure of the portfolio is 0.

Option Portfolio Sensitivity

Sorry, don't know why this image is constantly getting rotated but if you don't mind bending your neck, you will truly appreciate the Greeks math behind the portfolio. :). Also, BTW my handwriting is not bad, it's actually the font I am using which might not be the best as per the taste of the reader. :)

I hope you enjoyed reading it.

-Nitin

CDO - Collateralized Debt Obligations

What is a CDO?

CDOs are structured products created using financial engineering. These are products which are backed by cash flow from some sort of debt securities.

Securitization: It is a process of structuring the future cash flow in a more systematic manner such as getting coupons from bonds of various maturities and creating a single product with only one date for cash flow distribution to investors.

Under the CDO hood, anything can reside that has cash flow stream attached to it. You can think any bonds, loans such as credit card loans, auto-mobile loans, Mortgage loans etc.. can be used to create the CDO.

So, how is CDO created and structuring of cash flow works?

Usually a Bank has many loans with different customers. Banks want to get rid of these loans from their portfolio books. Some of these loans can be very risky but banks don't care about that part. They just want to get rid of these loans from their books. So, here is the process of creating the product.

1. Bank will bundle all the loans into one big chunk. Let's say the total value is 100 Million.

2. Bank will divide the bundle into multiple parts and these parts are called Tranches. The top most part is called Senior Tranche which usually has AAA rating. Other tranches are called Subordinate/Mezzanine tranches and will carry their own credit ratings.

3. Last tranche is called Equity tranche which almost never has any rating. Also, this tranche is usually still held in bank's books

Let's take a scenario where all the original 100 Million dollars loans were very risky loans and they all carried  BBB rating which means the loans might default any time. Now, banks use financial engineering process to create a AAA security from BBB security and that's innovation.

All the tranches carry 2 sources of income. Interest Income and/or Principal Income. They all carry one main Risk which is Default Risk and that is the most important risk.

Cash flows are distributed from the most senior tranche (AAA) to the most junior tranche (Equity). But losses are distributed from most junior (Equity) to the most senior (AAA) tranche.

Since BBB rating will provide higher yield than AAA due to its riskiness, banks usually try to create the AAA tranche with most amount of the CDO amount so that they have to pay the least interest to the tranche investors and can keep most of the interest income in the equity tranche (see below).

Let's imagine the original BBB bonds worth 100 Million were broken as follows under CDO:

60M - AAA (Senior Tranche) (Tranche A)                          Interest Offered (3%)

25M - BB (Second Tranche)  (Tranche B)                           Interest offered (6%)

15M - Equity Tranche (Usually Denoted as Tranche Z)          All residual goes here

Now the cash flow will be distributed as this:

Bank receives 8M in the interest income (8% of 100 M and considering no one has defaulted)

Bank will usually charge a service fee for processing payments (Can be anywhere 8-10% of yearly interests received)

Let's say Bank now has 7 Million to distribute

Bank will give 1.8M to Tranche A (3% of 60M)

Bank will give 1.5M to Tranche B   (6% of 25M)

Bank will give 3.7M to Equity Tranche so Equity tranche keeps on increasing in value

As you can see, banks love Securitization process. Why?? Because first they write bad loans and charge customers the loan origination, service fee and other fees plus some more fees. Now they package all these loans and sell them as CDOs and get their cash back that they lent to original customers plus they charge CDO investors also fee such as CDO origination fee, trustee fee, administration fee, and more fees. Additionally, with every cash distribution, they pay themselves first for processing the cash flow before investors see any cash. In the end, Banks make money while everyone else might be losing.

This securitization process was what caused CDO market collapse in America where CDO tranches were rated as AAA while underlying securities were BBB and AAA started to default which according to AAA definition should not have happened to that massive scale.

Key note is - Banks will find a way to offload their risk to another investor and make money. Bank love this process. So, be sure to understand the key characteristics of the underlying security before buying structured securities. Understand the Risk before understanding the Promised Returns

-Nitin

Debt and Equity Valuation using Option Pricing

Debt and Equity Valuation using Option Pricing:

Here, I will talk about how to value Debt and Equity of the firm using Option Pricing formula and the heart of Option Pricing Put-Call Parity.

Asset of the firm can be defined as the total value of its Debts and Equity.
Hence, Assets = Debt + Equity ---------------(1)

Using Put Call Parity from Black Scholes and Merton,
Call Option + PV (Strike) = Underlying + Put Option (Strike)  -----------(2)

Now, PV(Strike) can be thought of a Risk Free Bond that has the same face value as Strike price so you are confident that you have the money K at expiration. K is thought of the total DEBT value that firms owes to its debt holders at maturity. Underlying in this scenario can be treated as the assets of the firm itself. So, equation (2) can be re-written as:

Call + Risk Free Bond = Asset + Put Option --------------------(3)
From Equation (1), Debt = Asset - Equity --------(4)
Equity holders are nothing but Call holder with the strike as K as once the Debts are paid off, Equity holders own everything in the firm.
So, Debt = Asset - Call Option -------------------(5)

Using Call valuation from Equation 3, we can re-write, equation 5 as:
Debt = Asset - (Asset + Put Option - Risk Free Bond)

Debt = Risk Free Bond - Put Option ----------------------(6)

Which makes sense also, as Debt holders have their payoff maxed at K if firm value >= K else they own the assets which should be K - Put Pay off

Below image might make this intuitive sense clearer.

Similarly, Equity Holders can be valued as:
Equity = Asset + Put Option - Risk Free Bond --------------------------(7)

Intuitively, you can think of Equity Holders own the Asset and Put option to sell the assets after paying off the Debts (Risk Free Bond).

Nitin

What is Private Equity

What is Private Equity ?

These are private investments made by private firms mostly (except couple of public trade companies such as KKR) who want to acquire other companies. Once they acquire them, they unlock the value and resell them to other buyers such as IPO or just any other buyer.

Structure of Private Equity is as follows:

"Private Equity" PE Firm owns a fund called "Private Equity Fund" and this fund owns the ultimate "PE Portfolio companies". Portfolio companies are the same companies that PE firm is trying to acquire using the PE Fund.

Life cycle of the PE fund is as follows:
PE firm raises and manages the investment made by investors by being the General Partner of the fund. Core investors are Limited Partners such that their liability is capped to the invested capital and they are not responsible for manager's activities.

A PE Firm acquires the new firm through 2 ways
1. Acquisition through Equity of Portfolio Companies
2. Acquisition through Debt of Portfolio Companies

• Type of investment under Equity Category are: "Venture Capital" and "Leverage Buyout (LBO)" 
• Type of investment under Debt Category are: "Mezzanine Financing" and "Distressed Debt"

GPs of the PE firms usually charge a money management fee (1-3.5%) on yearly basis (Fixed Fee) and an incentive fee (around 10-30%) of the realized profits during exit of the fund.

I will write more on 4 types of investment categories in another post another time.

Nitin

Counterparty Credit Risk

What is Counterparty Credit Risk

Counterparty Credit Risk is all about risk of dealing with banks. This risk primarily deals with an event under which a banking institution (aka counterparty) fails to meet its obligations to return the money that it borrowed from another bank (aka counterparty).

Banks usually need a lot of cash to do trading, to run their operations, payroll etc... due to their gigantic size. Since they don't have all the cash handy, they usually go to another bank and borrow. Under good economic conditions, banks usually have no problems in lending each other money but they want some sort of assets in the escrow account to make sure they get their money back. The asset that is put as a guarantee in escrow account is called "Collateral". Once the borrower bank returns the money back, the lending bank returns the collateral.

Now consider, economic conditions start worsening and banks still need money to run their operations. The same original banks are now reluctant to lend each other because they are doubting whether the other bank will be able to pay the money back. In case, the borrowing bank doesn't return money, lending bank might have a problem with its operations as well. To signal other bank about its creditworthiness during bad economic conditions, borrowing banks are willing to put even more collateral to get the money. However, even after more collateral deposits, banks are still unwilling to lend each other due to counterparty risk. The rationale here is banks usually put Bonds as a collateral to borrow money and lending banks are not willing to keep those bonds as collateral because they are not even sure whether they would be able to recover 100% of the lent money by selling those bonds in case counterparty defaults on its obligation. Also, under bad economic conditions prices usually fall and hence it makes it even more difficult to price those bonds accurately. Seeing so much volatility in markets, banks usually decline to lend regardless of collateral being posted.

As one can see, when banks stop lending each other because of the creditworthiness of the borrowing bank, it can cause huge liquidity crisis in the financial sector. In fact, this was the primary reason why two famous banks in America, "Lehman Brothers" and "Bear Stearns" collapsed as no other bank was willing to give them cash to keep them functioning. Finally, without much cash in hands to run the operations, banks were left with no choice but to file bankruptcy.

Finally, Remember that Banks are institutions who will give you the umbrella on a perfect sunny day and  would want it back on a Rainy day.

This is what counterparty risk is all about.

Nitin  

Discount Factor

Discount Factor

Another key term in Finance Theory is Discount Factor. This factor tells you how future values should be discounted to get back to Present Value. Simplest way to understand Discount Factor is how much money I need today to get some pre-determined amount that I need in future. Example - you have a series of liabilities such as tuition fee for your kid which might be fixed at the end of every year, say $30,000. So, you have 4 years of liabilities of $30,000 each at sometime in future and you want to know how much money do you need today to offset these liabilities. Discount factor is your answer to such a question.

Discount factor has 2 dimension attributes. One is time and second is Interest Rate. Based on interest rate, your discount factor changes. A simple logic is higher the interest rate that bank offers, the lower the deposit you need today.

Discount Factor is calculated as 1/(1+r)^n Where n is the number of years and r is the interest rate that bank is offering on fixed deposits for that duration.

Below screenshot shows how discount factor changes with maturity and interest rate.

     Discount Factor 2-D Ladder

Now, to answer the original question on how much money you need to have 30,000 in future can be calculated as follows:
Let's say you need to have 30K in year 7, 8, 9, and 10 and the corresponding interest rates that bank offers are 7%, 8%, 9%, and 10%. Now you need to look at the intersection of maturity and interest rate to determine the correct discount factor for multiplication.
Discount factors that match maturity and interest rates are: 0.6227, 0.5403, 0.4604, 0.3855. Now to find total needs today, you just simply multiply each discount factor with the $30,000 that you need.
7 Yr = 18,681, 8 Yr = 16,209, 9 Yr = $13,812, and 10 Yr = $11,565.

So, altogether you would need a total of $60,267.00 today to offset your future liabilities of $120,000.
This is all about power of compounding where money keeps on making money. :)

-Nitin  

TVM - Time Value Of Money

Time Value of Money

One of the most fundamental concepts in Finance Theory is Time Value of Money. This concept is so crucial that without understanding and applying it correctly, none of the financial models be able to produce reliable outcome.

So, what is time value of money (TVM)?
This concept describes that money at two different time points is not same since money earns interest over that time period (money earns money). Let's say 1 year interest rate on fixed deposits on US Dollar is 10%. So, it's same as having $100 today vs $110 a year from now.

The reason why this concept is so important to us as an investor is we need to make an investment decision. Should we invest today or should we wait a year from now when we have 10% more money in hand? It's not that easy to answer but using some assumptions, a decision can be made.

Example: you have $100,000 today and you want to buy a house. The house costs $200,000. You have a choice of putting 100K down today and finance 50% or buy the house in a year from now with 55% down payment assuming nothing else has changed which usually doesn't happen. (House price can go up or down, inflation can skyrocket or etc... etc...)

In finance, value of money today is known as "Present Value" and value of money in future is called "Future Value". The interest income is called "Carrying Benefits" or plain "Interest Income" or "Time Value of Money"

Another one of the most important terms that is used in TVM is called "Discount Factor".

In above example as you might notice, that you give $100 today to receive $110 in a year can also be expressed as you give $90.91 today to receive $100 in a year from now. (They are same things)

Discount factor is calculated as PV/FV

In above example, 100/110 = 0.9091. In finance, we say it as 1 Year Discount factor at 10% is 0.9091.
To better use this information, the question can be asked as how much money do I need to deposit today in the bank to receive $525 in a year from now. You simply multiply your future value with the discount factor to get the answer. So, in this case you multiply 525 * 0.9091 = $477.27. In other words, you deposit $477.27 today and the bank will give you $525 in a year from now.

-Nitin

What Does Inflation Hedge mean?

What is Inflation Hedge? 

You ever heard in the media that Gold is inflation hedged instrument? I am sure many of us have heard this expression many times over CNBC, CNN Money etc.... So, what does Inflation Hedge mean?

In the last couple of posts, I have been mentioning that inflation is nothing more than measuring strength of the currency buying power. If currency gets weaker, we say inflation is higher since our buying power has deteriorated. So, how do we hedge ourselves against it.

It's really not that difficult and a it's very simple logic. It's just investment media make it sound so fancy and complicated such that local public get lost in financial terms. So, back to basics of Inflation - If the currency is getting weaker, people would have to pay a higher price for the same product in future as they pay for it today. So, why not hold something today that people would want to buy tomorrow such that you can collect a higher economic value in future. So, if you can own a lot of things today that people would want to buy tomorrow then you can only get richer in nominal terms in future.

Again back to economics, you have limited supply of cash inflow so you must use it wisely. Once cash is spent, you would have to wait for new cash which might take one month if you get paid monthly or who knows how your cash flow situation is. So, any asset that you think will be in demand in future can be bought with the money in hand today and you will be inflation hedged.

Also, when you buy an asset today, you need to consider following things as well:
1. Does buying the asset today has additional costs attached with it to store? In finance, we call it carrying cost. Hence, buy an asset that will have almost no storage costs.
2. You shouldn't buy an asset that may not be in demand in future because you wouldn't be able to charge more in future and hence will have negative return on your invested amount. This is called diminishing time value of money.

So, considering about principles, you wouldn't want to buy a lot of coke or pepsi bottles, or even gallon of gasoline, or anything that has a lot of storage overhead. So, what should one buy to hedge against inflation?

Some of the following assets are treated one of the best inflation hedged instruments.
1. Real Estate. (No storage is needed here)
2. Precious Metals such as Gold or Silver Bars (You can store them in the drawer, if needed)
3. Long term Futures Call Options on Oil Contracts. (Financial contracts carry counterparty credit risks)
4. DO NOT hold cash currency because that is the first one which loses value during inflation

Key note is: These instruments must stay in demand in future, else you might lose value of your invested capital. For example, if all of a sudden Gold demand dies out due to a cheaper substitutes availability in future, Gold price might fall down higher than inflation. Example holding a gold bar which lost 25% in its value due to demand evaporation while inflation was only 2%. You would lose 23% of your investment in such case.

Also, inflation hedge doesn't mean that you will always be richer in future in nominal terms than what you are today. There are many other types of risks that can eventually evaporate your wealth.

-Nitin 

Inflation - How do we measure it?

Inflation - How do we measure it?

In the last post, I described that inflation is nothing more than the strength of the currency. In the previous post, I used a cross currency reference of Australian Dollar and US Dollar to describe the relative purchasing power of Australians vs Americans. In this post, I will describe the relative strength of currency between two time periods at the national level.

In order for one to measure the strength of the currency in the domestic land between two time points, following parameters are needed:

a) Starting time point (usually denoted as t0 and often referred as reference point)
b) Future time point (any time in future, when inflation needs to be measured)
c) An Underlying(s) whose price needs to be measured usually called commodity basket or just basket.

Now, in order for us to measure the strength of the currency, we should take a good sample of products that  can help represent the inflation accurately.

Let's say a regular consumer has a dependency on following products

1. A gallon of Milk
2. A gallon of Gasoline
3. A 2 Litre bottle of Coke
4. A 32 inch television

I am taking a very small sample to get the point across but you can imagine that governments must consider all sorts of products that can accurately represent the domestic economy such as price of chicken, train ticket to New York City from Boston and so on.

Now, the above 4 products called the basket and their price is called Basket price. Imagine, our reference point is 2012 and hence we need the price of this basket on Jan 1, 2012 and Jan 1, 2013.

For simplicity, I am assuming uniform weights of these commodities in the economy and assuming that these 4 products accurately represent the economy.

Item             Jan 1, 2012             Jan 1, 2013
Milk             $5.00                      $4.50
Gasoline       $2.75                      $3.20
Coke            $2.00                      $3.50
TV               $100.00                  $101.00
===============================
Basket          $109.75                  $112.20
Price
===============================
So, the basket is 2.23% more expensive on Jan 1, 2013 when compared against same products on Jan 1, 2012. This will be known as yearly inflation.

Basket price is also known as Price index. In United States, it's called CPI (Consumer Price Index) where Index means the basket price of a bunch of commodities that US Govt uses as a reference basket to accurately represent health of economy.

Governments don't like higher inflation because it makes their currency weaker on a relative scale basis and hence they would intervene at various levels to control the relative strength of the currency.
Governments control inflation due to following 2 simple facts:

1. When currency becomes very expensive, exports takes a beating because the currency becomes very expensive for outsiders.
2. When currency gets cheaper, importers take a huge beating and these prices need to pushed down to the end consumer and consumers don't like to pay higher prices.

That's it for tonight.
Nitin 

Inflation - What is it?

Inflation - What is it?

So, what is inflation? what role does it play in our daily life. Did you ever wonder why a bottle of Coke that used to cost $1.20 now costs $2.25 or for that matter any other price. Usually products such as commodities offer the same functional value yet their economic value changes. For example, a bottle of coke still serves as a bottle of coke yet you have to pay a much higher price today. This is exactly what Inflation is all about. It's not the price of the underlying asset is increasing, it's because the buying power of your currency has gotten weaker and hence you must pay more of the weaker currency to buy exactly the same product.

Below example illustrates this concept a little better. I am using a cross currency example to illustrate it better.

Let's say an Australian Company charges AUD 100 for 1 gram of Gold. Also, in the foreign exchange market USD to AUD exchange rate is 1:1. Hence, for an American buyer, he needs to pay 100 US Dollars to buy the very same amount of 1 gram of gold.

Scenario 1: Let's imagine due to some government policies, USD has weakened against AUD and new exchange rate is: USD/AUD = 0.50 which means in 1 US Dollar now you get only 50 Australian Cents. This means US Dollar or anyone who is holding US Dollar in the pocket now has less buying power compared to when the exchange rate was 1:1. For the same American buyer to buy the very same 1 gram of gold, he now has to spend 200 USD. This is called Inflation where the buying power of the currency becomes weaker and everything priced in that currency must have a higher price when compared with old price.


Scenario 2: Let's imagine due to some government policies, USD has strengthened against AUD and new exchange rate is: USD/AUD = 2.0 which means in 1 US Dollar now you get you 2 Australian Dollars. This means US Dollar or anyone who is holding US Dollar in the pocket now can enjoy life with better life style. For the same American buyer to buy the very same 1 gram of gold, he now has to spend 50 USD only. This is scenario is Inflationary for Australians where the buying power of Australians now have weakened down against US Dollar.

Nitin

Money Vs Currency

Money Vs Currency

I thought of writing this blog after seeing a lot of buzz in the media such as "Federal Reserve is Printing Money" and right after that Media will show the printing press in US that is printing US Dollar bills.

It surprises me how simple it is to confuse Money vs Currency. Money is completely unreal, no one can touch it and yet in day to day life, we confuse it with currency. Money is not currency. Money is this imaginary, unreal concept that only helps us determine economic value of an asset such as the output of the country aka GDP, or economic value of labor force in the country.

These unreal, imaginary things are difficult to grasp at first when you hear about it but then a while later they start making perfect sense. For example, all the English alphabets are unreal, imaginary but when they are attached to something such as "Apple", "Boy", or "Charlie" and so on, these imaginary alphabets start making sense.

So, back to Money vs Currency - Money is unreal but when you assign a currency such as US Dollar to the United Stated GDP, it becomes real. Money can't be held in hands while currency can. One can't hold 10 Money in the pocket but one can hold 10 dollars or 10 Pounds in the pocket.

Log Returns Vs Normal Returns

Log Returns Vs Normal Returns

So, why there is so much hype about Log Returns, Normal Returns in the investment community? What do these returns mean and why we need to worry about them? Where do they get used and why do we need to convert from one form to another or vice-versa??

We as finance savvied are used to announce few difficult terms in the community such as heteroskedasticity, homoskedasticty and so on to earn some respect in the community (show off mostly or show how cool are we).

The return concept mentioned in the Blog does have some strong meaning in finance community and it makes life much easier while making investment decisions or doing financial modeling.

So, what are these return types and why do we worry about them?
Let's start with an example:

You invested $100 today and earned 12% return in year 1, 15% in year 2, 23% in year 3, 10% in year 4 and 18% in year 5. Now, if someone asks you what was your total accumulated return in these 5 years? The traditional way to calculate this (trust me, you don't need to be a Math Savvy for this) is as follows:
(1.12) * (1.15) * (1.23) * (1.10) * (1.18)  - 1 = 1.05 * 100 (Converting Decimal to Percentages) = 105% or an average of 21% per year.

Now, imagine there exists another yearly return series in which numbers are added and not multiplied in order to get the cumulative effect. We call that return series as continuous compounding series where returns are added and not multiplied. Key point is, these numbers are not same but they bring out the same final outcome. In Mathematics, it's called continuous compounding which is different than Discrete compounding.

Here is how you calculate one from another.
In the example above, 12%, 15%, 23% etc... are all Discrete returns and we can convert them to continuous compounded returns as follows:

Here is a little bit math behind it so excuse me for that:

You simply add 1 to the original return in decimal format and take Natural Log for it to convert to continuous compounded return.
So, 12% = Ln(1.12), 15% = Ln(1.15), and 23% = Ln(1.23)

Upon calculation,
12% = 11.33%
15% = 13.97%
23% = 20.70%

Now, one can simply add them to find multi-period continuous return. If you then want to know the SIMPLE return, you need to take the exponent of the final number.

Let me show you how this works mathematically and how multiplications are converted into additions:

For t periods Simple Returns:
1 + R (0, t) = (1+R1) * (1+R2) * (1+R3) * (1+R4)*.........*(1+Rt)  ----------(1)

Now, taking Natual Logs on both sides:
Ln(1+R(0,t) ) = Ln[(1+R1) * (1+R2) * (1+R3) * (1+R4)*.........*(1+Rt)  ]  ------------(2)

Logs have the property of converting multiplication into addition and it is this property which makes this concept so simple and yet highly innovative

Ln(1+R(0,t)) = Ln(1+R1) + Ln(1+R2) + Ln(1+R3) +...............................+ (1+Rt) ------------(3)

Let's Say using Logarithmic series, you found out what was the final sum on the right side, then all you need to do is:

Ln(1+R(0,t)) = x ----- where x is the final solved value from the express on right side of equation (3)

Taking Exponential on Both sides,
1+R(0,t) = Exp(x)

and R(0,t) = Exp(x) - 1

Primary use of such application is in Financial Modeling where a lot of numbers need to be manipulated and computer programs work much faster for additions than multiplications. Moreover, computer variables have tendency to produce arithmetic overflow errors when precisions go too far and as you know, precisions only go over in multiplications and divisions BUT NOT  in additions and subtractions so this techniques helps a lot.

Now, how to use Natural Log and Exponents is another question for another time but I hope you liked the concept.