Return, Risk, and the SML RWJ-Chapter 13

Returns Dollar Returns the sum of the cash received and the change in value of the asset, in dollars. Dividends Ending market value Time 1 Initial investment Percentage Returns the sum of the cash received and the change in value of the asset divided by the original investment.

Holding Period Return (Simple Return)   OR   Capital Gain Dividend Yield

HPR (Simple Return)-Example Suppose you bought 100 shares of Wal-Mart (WMT) one year ago today at $25. Over the last year, you received $20 in dividends (= 20 cents per share × 100 shares). At the end of the year, the stock sells for $30. How did you do? What is your return on this investment? Quite well. You invested $25 × 100 = $2,500. At the end of the year, you have stock worth $3,000 and cash dividends of $20. Your dollar gain was $520 = $20 + ($3,000 – $2,500). Your percentage gain for the year is $520/2500=20.8%

$520 20.8% = $2,500 $520 gain Dollar Return: $20 $3,000 Time 1 -$2,500 1 -$2,500 Percentage Return: 20.8% = $2,500 $520

HPR (Simple Period)- Example Let’s look at Ford     Capital Gain=2.16%% Dividend Yield=0.54% Source=Yahoo Finance

HPR- Multiple Periods The holding period return is the return that an investor would get when holding an investment over a period of n years, when the return during year i is given as ri: Compounding Return: The cumulative effect that a series of gains or losses on an original amount of capital over a period of time

HPR (Multiple Periods)- Example (3) Suppose your investment provides the following returns over a four-year period:

Annualizing Return How can I annualize my return over time? Two ways: Arithmetic Average Geometric Average

Example Average (Arithmetic Return)? Geometric Return? Interpret the results Arithmetic Return: (10-5+20+15)/4=10 Geometric Return (1+r)^4=(1.10)*(0.95)*(1.20)*(1.15) => r=0.0958 an arithmetic average assumes that each return is an independent event. However, when it comes to annual investment returns, the numbers are not independent of each other. If you lose a ton of money one year, you have that much less capital to generate returns during the following years, and vice versa. Because of this reality, we need to calculate the geometric average of your investment returns in order to get an accurate measurement of what your actual average annual return over time

Risk: What is risk? Webster’s dictionary: “exposing to loss or damage” In finance: Stand-alone basis Portfolio basis

Which one is more risky? Why?

Risk and Return Relation: Is risk a bad?

Historical Returns, 1926-2014 Average Standard Series Annual Return Deviation Distribution Large Company Stocks 12.1% 20.1% Small Company Stocks 16.7 32.1 Long-Term Corporate Bonds 6.4 8.4 Long-Term Government Bonds 6.1 10.0 U.S. Treasury Bills 3.5 3.1 Inflation 3.0 4.1 – 90% 0% + 90%

How to measure Risk? Likelihood that investors will receive a return on an investment that is different from the return they expected to make Two important key words in this definition Expectations Deviation from our expectations

To measure Risk: We need to know two concepts? TIME SERIES ARE GIVEN Expected Return: How much “actual return” deviates from “Expected Return”?   Expected Return   Variance

To measure Risk: We need to know two concepts? PROBABILITY DISTRIBUTION GIVEN Probability: The chance that event will occur Probability Distribution: If all possible events, or outcomes, are listed, and if probability is assigned to each event, the listing is called probability distribution.

Then: Expected Return: How much “actual return” deviates from “Expected Return”?   Expected Return   Variance

Example What is the expected return of Stock X?      

d4 d1 d3 d2   Standard Deviation

The Risk-Return Tradeoff

Risk Statistics There is no universally agreed-upon definition of risk. The measures of risk that we discuss are variance and standard deviation. The standard deviation is the standard statistical measure of the spread of a sample, and it will be the measure we use most of this time. Its interpretation is facilitated by a discussion of the normal distribution.

Normal Distribution A large enough sample drawn from a normal distribution looks like a bell-shaped curve. Probability The probability that a yearly return will fall within 20.1 percent of the mean of 12.1 percent will be approximately 2/3. – 3s – 48.2% – 2s – 28.1% – 1s – 8.0% 0 12.1% + 1s 32.2% + 2s 52.3% + 3s 72.4% Return on large company common stocks 68.26% 95.44% 99.74%

Interpretation of Risk The 20.1% standard deviation we found for large stock returns from 1926 through 2014 can now be interpreted in the following way: If stock returns are approximately normally distributed, the probability that a yearly return will fall within 20.1 percent of the mean of 12.1% will be approximately 2/3.

Diversification and Systematic Risk What is diversification? Spreading a portfolio over many investments to avoid excessive exposure to any source of risk

Diversifiable vs. Market Risk To the extent that the firm specific influences on two stocks differ, diversification should reduce portfolio risk With all risk sources independent, the exposure to any particular source of risk is reduced to a negligible level Firm specific risk is called unsystematic, unique risk, idiosyncratic risk, or diversifiable risk The risk remains even after extensive diversification. This risk is called market or systematic risk

Factors Affecting Unsystematic and Systematic Risk Unsystematic (Unique) Risk: Successful or unsuccessful product or marketing program Winning or loosing of a major contract In particular: good or bad news for a firm Systematic Risk: Economic conditions; recession, boom, high inflation, high interest rates

Diversification Unique Risk Systematic Risk

Market Risk How sensitive a stock to market factor (macroeconomic factor). Market portfolio is a portfolio made up of all the assets in the market

Summary: Based on the studies on capital market history, we know that there is reward, on average, for bearing risk. Since, unsystematic risk can be eliminated at virtually no cost (by diversifying), there is no reward for bearing it. Put another way, the market does not reward risks that are borne unnecessarily. Implication: The expected return on an asset depends only on that asset’s systematic risk No matter how much total risk an asset has, only the systematic portion is relevant in determining the expected return No matter how much total risk an asset has, only the systematic portion is relevant in determining the expected return

How to Measure Systematic Risk? Estimation of Beta   Beta is a measure of stock’s volatility in relation to the market or the responsiveness of a security to movements in the market portfolio (i.e., systematic risk). Estimation made using t=1, 2, 3, … ,T

Example-Expected Return of a Portfolio You have $10,000, what is your portfolio return if you invest $2000 in Stock X (Beta X=2) and $8000 in Stock Y (Beta Y=0.5). Let’s assume expected return for Stock X and Stock Y is 20% and 10% respectively. What is the expected return of Portfolio? What is the expected Beta of Portfolio?

Portfolio Beta and Security Market Line Weighted average Betas of the stocks in the portfolio SML: Expected Return and Systematic Risk Relation:  

How to measure systematic risk? Because systematic risk is the crucial determinant of an asset’s expected return, we need some way of measuring the level of systematic risk for different investment. β (Beta Coefficient) tells us how much systematic risk as an average asset Market Beta=1 Risk Free Rate Beta=0 Stock A: Standard Deviation=40%, Beta=0.50 Stock B: Standard Deviation=20%, Beta=1.50 Ford: http://www.google.com/finance?q=ford&ei=pISCUtCmIoG20AH2PA

Example (7) Let’s assume that you have a market portfolio (S&P 500) and risk- free rate asset (T-bills). Expected rate of Market Portfolio is 10% and risk-free rate is 3% What is the expected return and Beta if you invest: 100% in risk free rate 75% in risk free rate and 25% in Market Portfolio 50% in risk free rate and 50% in Market Portfolio 25% in risk free rate and 75% in Market Portfolio 100% in Market Portfolio

  E(Ri)-rf/beta-i=E(Rm)-rf   Market Risk Premium

The SML and the Cost of Capital: A Preview Risk is an extremely important consideration in almost all business decisions. Therefore, we need to the find the relation between risk and return (the SML) We also need to know what determines the appropriate discount rate for future cash flows: Market risk premium, risk free rate and Beta Why is the SML important: It tells us reward to risk in financial markets In order to find the discount rate: we need to compare the expected return on that investment to what the financial market offers on an investment with the same beta. In other words, the SML line tells us the “going rate” for bearing risk in the economy.

The SML and the Cost of Capital: A Preview Cost of Capital: the appropriate discount rate on a new project is the minimum expected rate of return an investment must offer to be attractive This minimum required rate of return is called “Cost of Capital” We have a much better idea of what determines the required return on investment.