Homework answers / question archive / -1- Describe the following terms — explain, add a short example, and a formula where relevant: -a- Arithmetic average -b- Average compounded returns -c- Variance -d- Diversification -e- Beta  -2- Solve for: -a- Ch 7 Questions 7, 12, 19, 22 (make sure to explain your answer for b)

-1- Describe the following terms — explain, add a short example, and a formula where relevant: -a- Arithmetic average -b- Average compounded returns -c- Variance -d- Diversification -e- Beta  -2- Solve for: -a- Ch 7 Questions 7, 12, 19, 22 (make sure to explain your answer for b)

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-1- Describe the following terms — explain, add a short example, and a formula where relevant: -a- Arithmetic average -b- Average compounded returns -c- Variance -d- Diversification -e- Beta 
-2- Solve for: -a- Ch 7 Questions 7, 12, 19, 22 (make sure to explain your answer for b). 

7. Expected return and standard deviation A game of chance offers the following odds and payoffs. Each play of the game costs $100, so the net profit per play is the payoff less $100. 
Probability 
Payoff Net Profit 
0.10 $500 $400 0.50 100 0 0.40 0 -100 
What are the expected cash payoff and expected rate of return? Calculate the variance and standard deviation of this rate of return. (Do not make the adjustment for degrees of freedom described in footnote 15.) 

12. Diversification* Here are the percentage returns on two stocks. a. Calculate the monthly variance and standard deviation of each stock. Which stock is the riskier if held on its own? b. Now calculate the variance and standard deviation of the returns on a portfolio that invests an equal amount each month in the two stocks. c. Is the variance more or less than half way between the variance of the two individual stocks? 
Month 
Digital Cheese Executive Fruit 
January February February March April May June 
+15% —3 +5 +7 —4 +3 July —2 August —8 

1 
19. Portfolio risk Your eccentric Aunt Claudia has left you $50,000 in BP shares plus $50,000 cash. Unfortunately, her will requires that the BP stock not be sold for one year and the $50,000 cash must be entirely invested in one of the stocks shown in Table 7.8. What is the safest attainable portfolio under these restrictions? 
22. Stock betas There are few, if any, real companies with negative betas. But suppose you found one with 13 = —.25. a. How would you expect this stock's rate of return to change if the overall market rose by an extra 5%? What if the market fell by an extra 5%? 
Stock Return if Market Return Is: 
A 0 +20 B —20 +20 C —30 0 D +15 +15 E +10 —10 
)TABLE 7.9 Stock betas. See Problem 21. 
b. You have $1 million invested in a well-diversified portfolio of stocks. Now you receive an additional $20,000 bequest. Which of the following actions will yield the safest overall portfolio return? i. Invest $20,000 in Treasury bills (which have p = 0). ii. Invest $20,000 in stocks with 13 = 1. iii. Invest $20,000 in the stock with 1 = —.25. Explain your answer.