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LIBOR Finance 101

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Finance Finance deals with the concepts of time, money, risk and how they are interrelated It also deals with the task of providing funds for a corporations activities It describes the management of money, banking, credit, investments and assets

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Time Value of Money “A dollar today is always worth more than a dollar tomorrow” The idea is that money available today is worth more than the same amount in the future due to the potential for earning interest You can simply invest the dollar you got today in the bank to earn interest So if I earn 5% interest per year, today’s dollar will be worth $1.05 in one year; as opposed to a dollar that I get in one year and that is still worth $1

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Time Value of Money So now say that I have to choose between $148 today and $156 a year from now, given that the interest rate is still 5% Therefore I need to find the Present Value of both of these sums and compare them Present Value is the current worth of a future sum of money Back to the first example: the Present Value of $1.05 received one year from now, assuming an interest rate of 5% is $1 as we already worked out Present Value = Future Value / (1+i)^t

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Time Value of Money t = number of years, given that your interest is an APR Future Value = the amount that you will receive in the future This concept can be extended to value more than just sums of money

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Net Present Value The value of any asset is the Present Value of its future cash flows We just expand on our PV formula We will have a series of cash flows, each of which we will need to discount to arrive at a present value Then you sum these present values to arrive at NPV

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Net Present Value I invest $100 in a project, in year one it returns $150 and in year two it returns $200; assume 5% These are future values so I need to discount them to the present values, I use the interest rate to discount my cash flows This 5% interest rate is the rate that I could earn if I had invested that $100 elsewhere 150/(1.05^1) + 200/(1.05^2) – 100 Note that we do not discount the 100 dollars I just spent on the project, that is because I just did so; it is not a future value = $224.27

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**Net Present Value So what does this mean?**

If my NPV is greater than 0, it is better to invest in my project As long as there is not a project with a higher NPV, I would invest in it

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**Internal Rate of Return**

If I set NPV to 0 and you leave the interest rate as a variable, the interest rate that you find is the IRR IRR is the interest rate at which the NPV of costs and the NPV of proceeds from an investment are equal The higher an IRR, the more desirable the project (not unlike NPV)

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Risk vs. Return Low levels of uncertainty are associated with low potential returns High levels of uncertainty are associated with high potential returns It is important to note that higher levels of risk do not guarantee higher returns, it only increases the possibility of higher returns Therefore invested money can return higher profits only it that money is subject to a higher possibility of being lost If you want to make money, you must accept some risk, the goal is to find an appropriate balance

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Risk vs. Return This graph shows the relationship

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Risk vs. Return On the low end of the scale, you see Rf or the risk-free rate of return This rate is represented by the rate of return on US Government securities, because they are considered to be riskless So if the risk-free rate is 3%, you are earning 3% on your investment while taking on no risk

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**Risk Risk is represented by the standard deviation of a portfolio**

Risk on any investment can be separated into two sources Risk that is specific to the firm is firm-specific, unique or unsystematic risk Risk that is not specific to the firm is market or systematic risk

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Diversification This is a risk management technique often mentioned in finance The general idea is to mix a wide variety of investments within a portfolio This will minimize the impact that any one investment may have on the performance of the portfolio Diversification can only reduce/eliminate unsystematic risk

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Diversification As you can see, as the number of securities in a portfolio increases, one can reduce unsystematic risk to the level of market risk

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Diversification Thinking about why the firm-specific risk is eliminated: Adding new investments means that each investment in my portfolio is now a much smaller percentage of my portfolio During any time period some firms may do well, while others do poorly; therefore, these effects will average out to zero This means that diversification will only benefit me if my investments are not correlated If I buy Apple and Microsoft I am not as diversified as if I buy Ford and Microsoft

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The Market Portfolio The limit of my ability to diversify is to hold a portfolio of every asset This is called the market portfolio It is assumed that every investor holds a combination of the market portfolio and a risk free asset The possible combinations are shown along the capital market line

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Capital Market Line As you move up and to the right, you are investing more in the market portfolio and less in the risk free asset

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Individual Risk The a portfolio setting, the risk of an asset is equal to the risk that it adds to the market portfolio This is measured by the covariance, or how much an asset moves with the market We measure this with Beta

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**Beta Beta is a financial variable that you will see a lot**

It measures the systematic risk for any asset It is measured by the covariance of its returns with the returns on a market index This means it is the tendency of a security’s returns to respond to changes in the market Or even simpler, it is the correlation of an investment with respect to the market If Beta: = 0, the returns of the asset change independently of changes in the market’s returns =1, the price of the asset moves with the market (so the market has a beta of 1) >1, the price will be more volatile (more risky) than the market <1, the price will be less volatile than the market

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**Beta For example: Beta is a key part of the CAPM model**

If Stock A’s beta = 1.2, that stock is 20% more volatile than the market So if the market goes up 10% next month, I would expect Stock A to go up 12% Beta is a key part of the CAPM model

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**Capital Asset Pricing Model**

This model will give me an expected rate of return for an asset The expected ror equals the required ror, I am determining my required return for investing in the asset (see risk vs. return) The expected return of a security equals the return on a risk free security plus a risk premium E(Ri) = Expected (required) return Rf = Return on a risk free asset Bi = Beta of the asset E(Rm) = Expected market return

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Security Market Line This graphs the results from the CAPM

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Security Market Line Undervalued stocks are above the SML because the investor would be accepting more return for the amount of risk assumed Overvalued stocks are below the SML because the investor would be accepting less return for the amount of risk assumed

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Random Walk Theory This theory states that the past movement of a stock price cannot be used to predict its future movement Stocks take a random and unpredictable path; the chances of a stock’s price to go up in the future is the same as it going down Believers in this theory hold that a long-term buy and hold strategy is the best This is not a popular concept on Wall Street because it largely goes against concepts such as analysis to find outperforming stocks

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**Efficient Market Hypothesis**

This hypothesis states that it is impossible to beat the market because prices of stocks already incorporate and reflect all relevant information This means that buying and selling securities is only a game of chance and not skill If markets are efficient, they reflect all information, so you can’t find mispriced stocks For obvious reasons Wall Street does not believe in this hypothesis

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**Sources http://pages.stern.nyu.edu/~wsilber/NPV%20Versus%20IR R.pdf**

Check out the other courses on Dr. Adamodar’s website as well, he posts much of the materials that a student in his class would receive Investopedia.com Wikipedia.com

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Chapter 6 Efficient Diversification Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin.

Chapter 6 Efficient Diversification Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin.

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