RWJ 10: Risk and Return: Lessons from Market History

Question 1

Suppose that you hold stock and don’t sell it at year end. Should you still consider the capital gain as part of your return? Does this violate our previous present value rule that only cash matters?

Answer 1

The capital gain is every bit as much a part of
your return as the dividend, and you should certainly count it as part of your total return. That you have decided to hold onto the stock and not sell, or realize the gain or the loss, in no way changes the fact that, if you wanted, you could get the cash value of the stock. After all, you could always sell the stock at year-end and immediately buy it back. The total amount of cash you would have at year-end would be the $518 gain plus your initial investment of $3,700. You would not lose this return when you bought back 100 shares of stock. In fact, you would be in exactly the same position as if you had not sold the stock (assuming, of course,
that there are no tax consequences and no brokerage commissions from selling the stock).

Question 2

Formula for Dividend Yield

Answer 2

Div(t+1)/P(t)

Question 3

Calculate Percentage Return

Answer 3

(Div paid at the end of period+ change in market value over period) / Beginning market value

OR

(Div paid at the end + market value at the end) / Beginning market value - 1

Question 4

Calculate holding period return

Answer 4

(1+R1)(1+R2)(1+R3)

Question 5

Define “excess return on risky asset”

Answer 5

Diff btw risky returns and risk-free return

Question 6

Define “equity risk premium”

Answer 6

Excess return on common stocks

Question 7

Calculate variance

Answer 7

1/(T-1)*(Ri - R mean)^2

Question 8

Calculate Sharpe Ratio/Reward to Risk Ratio

Answer 8

Average equity risk premium/ SD (it is a measure of return to the level of risk taken)

Question 9

For normal distribution, probability of having a return that is within 1 (and 2) SD of the mean is?

Answer 9

68% and 95%

Question 10

Difference between Geometric Average Return and Arithmetic Average Return *Suppose buy a stock for $100, 1st year falls to $50, 2nd year back to $100

Answer 10

GAR= [(1+R1)(1+R2)…..]^(1/T)-1
*What was your average compound return per year over a particular period

AAR= (R1+R2+……)/T
*What was your return in an average year over a particular period

GAR always smaller or equal(when all returns are identical) to AAR; The difference is greater for more volatile investments

Approximately, GAR=AAR-0.5Var

GAR is useful in describing the actual historical investment experience; AAR is useful in making estimates of the future (unbiased estimate of the true mean)

Question 11

Calculate Standard Error

Answer 11

SE=SD(R mean)=SD(R) / sqrt(#obs)
* How much confidence we can have in our R mean
+-2SE -> 95.4% confident that R mean is in the range

Question 12

Bottom line for future equity risk premium?

Answer 12

Any estimate will involve assumptions about the future risk environment as well as the amount of risk aversion of future investors

Question 13

What are the different asset classes we have studied in this chapter?

Answer 13

Small-company stocks, large-company stocks, long-term corporate bonds, long-term government bonds, intermediate-term government bonds, U.S. Treasury bills