Introduction to Risk and Return Where does the discount rate come from? Financial Management: lecture 7

Financial Management: lecture 7 Today’s plan Review of what we have learned in the last lecture Introduction to risk How to measure investment performance Rates of Return 73 Years of Capital Market History Measuring risk and risk premium Risk & Portfolio Diversification Two types of risk How to measure systematic risk CAPM Financial Management: lecture 7 2

What have we learned in the last lecture? Other two investment rules IRR Payback period rule Pay attention to: Depreciation Financing Incremental cash flows and opportunity cost Free cash flows or cash flows in finance Cash flows from operations Cash flows from the change of working capital Cash flows from capital investment and disposal Financial Management: lecture 7

How to calculate cash flows from operations? Method 1 Cash flows from operations =revenue –cost (cash expenses) – tax payment Method 2 Cash flows from operations = accounting profit + depreciation Method 3 Cash flows from operations =(revenue –cost)*(1-tax rate) + depreciation *tax rate Financial Management: lecture 7

Financial Management: lecture 7 Example revenue 1,000 Cost 600 Depreciation 200 Profit before tax 200 Tax at 35% 70 Net income 130 Given information above, please use three methods to calculate Cash flows Financial Management: lecture 7

Financial Management: lecture 7 Solution: Method 1 Cash flows=1000-600-70=330 Method 2 Cash flows =130+200=330 Method 3 Cash flows =(1000-600)*(1-0.35)+200*0.35 =330 Financial Management: lecture 7

A summary example ( Blooper) Now we can apply what we have learned about how to calculate cash flows to the Blooper example, whose information is given in the following slide. Financial Management: lecture 7

Financial Management: lecture 7 Blooper Industries (,000s) Financial Management: lecture 7 18

Cash flows from operations for the first year Financial Management: lecture 7 19

Financial Management: lecture 7 Blooper Industries Net Cash Flow (entire project) (,000s) NPV @ 12% = $3,564,000 Financial Management: lecture 7 20

How to measure the performance of your investment Suppose you buy one share of IBM at $74 this year and sell it at the expected price of $102. IBM pays a dividend of $1.25 for your investment What profit do you expect to make for your investment? What profit do you expect to make for one dollar investment? Financial Management: lecture 7

Financial Management: lecture 7 Solution Profit in total =102-74+1.25=$29.25 Profit per one dollar=29.25/74=0.395 or 39.5% Financial Management: lecture 7

Financial Management: lecture 7 Rates of Return Financial Management: lecture 7 5

Financial Management: lecture 7 Rates of Return Financial Management: lecture 7 6

Financial Management: lecture 7 Rates of Return Financial Management: lecture 7 8

Financial Management: lecture 7 Rates of Return Nominal vs. Real Suppose that the inflation rate is1.6% Financial Management: lecture 7 11

Financial Management: lecture 7 Market Indexes Dow Jones Industrial Average (The Dow) Value of a portfolio holding one share in each of 30 large industrial firms. Standard & Poor’s Composite Index (The S&P 500) Value of a portfolio holding shares in 500 firms. Holdings are proportional to the number of shares in the issues. Financial Management: lecture 7 12

The performance of $0.1 investment Financial Management: lecture 7

Volatility of portfolios Year Financial Management: lecture 7

Why are stock returns so high? To invest in stocks, investors require a risk premium with respect to relative risk-free security such as government securities. The expected return on a risky security is equal to the risk-free rate plus a risk premium Expected return =risk-free rate + risk premium Risk premium =expected return –risk-free rate Example 23.3% (1981 on market portfolio)=14%+9.3% 14.1% (1999 on market portfolio)=4.8%+9.3% Financial Management: lecture 7

Financial Management: lecture 7 How to Measure Risk We can use the variance or the standard deviation of the expected rate of return to measure risk. Variance or standard deviation measure weighted average of squared deviation of each observation from the mean. Financial Management: lecture 7 16

Financial Management: lecture 7 Some formula Suppose that there are N states, then the expected rate of return (mean) is The variance of the rate of return is The standard deviation Financial Management: lecture 7

Example of risk Stock A has the following returns depending on the state of the economy next year as follows: State of economy Probability of the state Return rate Good 0.6 20% 0.3 Average 10% 0.1 -5% Bad Financial Management: lecture 7

Measure risk (continue) First, calculate the mean return or the expected rate of return. Here N=3 (three states) Expected rate of return is r-bar= p1*r1+p2*r2+p3*r3=0.6*0.2+0.3*0.1+0.1*(-0.05) =14.5% The variance of return is p1*(r1- r-bar)2+p2*(r2- r-bar)2+p3*(r3-r-bar)2 =0.006225 The standard deviation is 0.078=7.8% Financial Management: lecture 7

Financial Management: lecture 7 Two types of risks Unique Risk - Risk factors affecting only that firm. Also called “firm-level risk.” Market Risk - Economy-wide sources of risk that affect the overall stock market. Also called “systematic risk.” Financial Management: lecture 7 18

Financial Management: lecture 7 Can we reduce risk? Yes, we can reduce risk by diversification: that is, we invest our money in different assets or form a portfolio of different assets. Can we understand intuitively why diversification can reduce risk? Financial Management: lecture 7

Financial Management: lecture 7 Portfolio weights Let W be the total money invested in a portfolio, a set of assets. Let xi be the proportion of total wealth invested in asset i. Then xi is called portfolio weight for asset i. The sum of portfolio weights for all the assets in the portfolio is 1, that is, Financial Management: lecture 7

Financial Management: lecture 7 Example You invest $400 of your $1000 in IBM at a price of $74 per share and the other in Dell at a price of $28. What is the portfolio weight for IBM and Dell respectively? Are you sure that you are right? Financial Management: lecture 7

Financial Management: lecture 7 Solution xIBM=400/1000=0.4 xDell=600/1000=0.6 xIBM+xDell=1 Financial Management: lecture 7

Some formula for portfolios The return of a portfolio is the weighted average of returns of the stocks in the portfolio. That is, The expected return of a portfolio is the weighted average of expected returns of the stocks in the portfolio. That is, Financial Management: lecture 7

Risk and Diversification (example) John puts his money half in stock A and half in stock B, as shown in the following. What is the mean and variance of the return of John’s portfolio? Financial Management: lecture 7

Financial Management: lecture 7 My solution The mean of the return of a portfolio is the weighted average of the returns of the stocks in the portfolio. Thus the mean of the return of John’s portfolio is The variance of the return of the portfolio is portfolio variance Financial Management: lecture 7

Risk and Diversification Financial Management: lecture 7 21

Financial Management: lecture 7 Measuring Market Risk Market Portfolio It is a portfolio of all assets in the economy. In practice a broad stock market index, such as the S&P 500 is used to represent the market portfolio. The market return is denoted by Rm Beta (β) Sensitivity of a stock’s return to the return on the market portfolio, Mathematically, Financial Management: lecture 7 3

An intuitive example for Beta Turbo Charged Seafood has the following % returns on its stock, relative to the listed changes in the % return on the market portfolio. The beta of Turbo Charged Seafood can be derived from this information. Financial Management: lecture 7 4

Measuring Market Risk (example, continue) Financial Management: lecture 7 5

Measuring Market Risk (continue) When the market was up 1%, Turbo average % change was +0.8% When the market was down 1%, Turbo average % change was -0.8% The average change of 1.6 % (-0.8 to 0.8) divided by the 2% (-1.0 to 1.0) change in the market produces a beta of 0.8. β=1.6/2=0.8 Financial Management: lecture 7 6

Another example Suppose we have following information: State Market Stock A Stock B -6% -8% -10% bad 24% good 32% 38% a. What is the beta for each stock? b. What is the expected return for each stock if each scenario is equally likely? c. What is the expected return for each stock if the probability for good economy is 20%? Financial Management: lecture 7

Financial Management: lecture 7 Solution a. b. c. Financial Management: lecture 7

Financial Management: lecture 7 Portfolio Betas Diversification reduces unique risk, but not market risk. The beta of a portfolio will be an weighted average of the betas of the securities in the portfolio. What is the beta of the market portfolio? What is the beta of the risk-free security? Financial Management: lecture 7 9

Financial Management: lecture 7 Example Suppose you have a portfolio of IBM and Dell with a beta of 1.2 and 2.2, respectively. If you put 50% of your money in IBM, and the other in Dell, what is the beta of your portfolio Beta of your portfolio =0.5*1.2 +0.5*2.2=1.7 Financial Management: lecture 7

Market risk and risk premium Risk premium for bearing market risk The difference between the expected return required by investors and the risk-free asset. Example, the expected return on IBM is 10%, the risk-free rate is 5%, and the risk premium is 10% -5%=5% If a security ( an individual security or a portfolio) has market or systematic risk, risk-averse investors will require a risk premium. Financial Management: lecture 7

CAPM (Capital Asset Pricing Model) The risk premium on each security is proportional to the market risk premium and the beta of the security. That is, Financial Management: lecture 7

Financial Management: lecture 7 Security market line The graphic representation of CAPM in the expected return and Beta plane Security Market Line Rm rf Financial Management: lecture 7 11