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

2. 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
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3. 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
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4. 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
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5. Financial Management: lecture 7
Example
revenue ,000
Cost
Depreciation
Profit before tax
Tax at 35%
Net income
Given information above, please use three methods to calculate
Cash flows
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6. Financial Management: lecture 7
Solution:
Method 1
Cash flows= =330
Method 2
Cash flows = =330
Method 3
Cash flows =( )*(1-0.35)+200*0.35
=330
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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.
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8. Financial Management: lecture 7
Blooper Industries
(,000s)
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9. Cash flows from operations for the first year
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10. Financial Management: lecture 7
Blooper Industries
Net Cash Flow (entire project) (,000s)
12% = $3,564,000
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11. 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?
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12. Financial Management: lecture 7
Solution
Profit in total = =$29.25
Profit per one dollar=29.25/74=0.395 or 39.5%
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13. Financial Management: lecture 7
Rates of Return
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14. Financial Management: lecture 7
Rates of Return
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15. Financial Management: lecture 7
Rates of Return
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16. Financial Management: lecture 7
Rates of Return
Nominal vs. Real
Suppose that the
inflation rate is1.6%
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17. 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.
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18. The performance of $0.1 investment
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19. Volatility of portfolios
Year
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20. 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%
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21. 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.
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22. 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
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23. 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
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24. 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* * *(-0.05)
=14.5%
The variance of return is
p1*(r1- r-bar)2+p2*(r2- r-bar)2+p3*(r3-r-bar)2 =
The standard deviation is 0.078=7.8%
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25. 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.”
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26. 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?
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27. 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,
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28. 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?
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29. Financial Management: lecture 7
Solution
xIBM=400/1000=0.4
xDell=600/1000=0.6
xIBM+xDell=1
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30. 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,
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31. 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?
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32. 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
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33. Risk and Diversification
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34. 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,
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35. 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.
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36. Measuring Market Risk (example, continue)
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37. 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 β=1.6/2=0.8
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38. 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%?
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39. Financial Management: lecture 7
Solution a. b. c.
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40. 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?
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41. 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* *2.2=1.7
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42. 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.
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43. 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,
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44. Financial Management: lecture 7
Security market line
The graphic representation of CAPM in the expected return and Beta plane
Security Market Line Rm rf
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