1. Midterm 2
Spring 2017

2. Problem 1
In a sample of three stocks, the annual rate of returns last year were 7%, 18%, and 35%. The standard deviation of this sample is__?
Answer:
𝐴𝑣𝑒𝑟𝑎𝑔𝑒= =.2
𝑉𝑎𝑟= 1 3− − − −.2 2
𝑉𝑎𝑟=.0199
𝑺𝒕𝒅𝑫𝒆𝒗= .𝟎𝟏𝟗𝟗 𝟏 𝟐 =.𝟏𝟒𝟏𝟎𝟔𝟕

3. Problem 2
Aeber purchased a zero-coupon bond earlier today for $500. The bond has a yield to maturity of 10% and matures in two years. If the bond now has a yield to maturity of 8%, what is the current bond value? Assume all yields are effective annual rates.
Answer:
𝑃𝑟𝑖𝑐𝑒=500= 𝐹𝑎𝑐𝑒 𝑉𝑎𝑙𝑢𝑒
𝐹𝑎𝑐𝑒 𝑉𝑎𝑙𝑢𝑒=500 1,1 2 =605
If YTM changes to 8% -
𝑷𝒓𝒊𝒄𝒆= 𝟔𝟎𝟓 𝟏.𝟎𝟖 𝟐 =𝟓𝟏𝟖.𝟔𝟗

4. Problem 3
Assume that the risk free return in the market is currently 10%, and a stock with beta of 5 has an expected return of 35%. What is the expected return on the market portfolio?
Answer:
CAPM:
𝑟 𝑟 = 𝑟 𝑓 +𝛽 𝑟 𝑚 − 𝑟 𝑓
.35=.1+5 𝑟 𝑚 −.1
𝒓 𝒎 = .𝟑𝟓−.𝟏 𝟓 +.𝟏=.𝟎𝟓+.𝟏=.𝟏𝟓

5. Using the information from the last problem:
Assume that the risk free return in the market is currently 10%, and a stock with beta of 5 has an expected return of 35%. What is the risk premium?
Answer:
Using the information from the last problem:
𝑟 𝑚 =.15
Risk Premium = 𝑟 𝑚 − 𝑟 𝑓
.𝟏𝟓−.𝟏=.𝟎𝟓

6. 𝑠.𝑒.= 𝑠𝑑 (𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑖𝑧𝑒)^(1/2) = .22 121 1 2 =.02
Problem 5
From Jan 1, 1890, to Jan 1, 2011, the historical average annual rate of return in the hypothetical county of Wachatame was 10%. The annual standard deviation of the rate of return was 22%. What is the upper bound of the 95.4% confidence interval for the annual rate of return based on this information? Hint: you need to be within two standard error of the average to find the upper and lower bounds of the 95.4% confidence interval.
Answer:
𝑢𝑝𝑝𝑒𝑟 𝑏𝑜𝑢𝑛𝑑=10%+2∗𝑠.𝑒.
𝑠.𝑒.= 𝑠𝑑 (𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑖𝑧𝑒)^(1/2) = =.02
𝒖𝒑𝒑𝒆𝒓 𝒃𝒐𝒖𝒏𝒅=𝟏𝟎%+𝟐∗.𝟎𝟐=.𝟏𝟒

7. Problem 6
A stock will pay its next dividend of $2 per share later today. The dividend over each of the next 5 years will increase by 20% per year. After that, the dividend will not change. Assume that dividends will be paid forever. What is the present value? EAR is 25%
Answer:
𝑃𝑉= −.2 − 1 .25− ∗ ∗ = Or
𝑃𝑉= ∗ =

8. If $100 is invested in each stock,
Problem 7
Suppose the Stock F and Stock G have a correlation value of rho=01. Stock F has an expected return of 20% and a standard deviation of 30%. Stock G has an expected return of 20% and a standard deviation of 30%. Today each stock is valued at $100 per share. Over the next year, Stock F will go up by $10. How much will Stock G go up by next year?
Answer:
If $100 is invested in each stock,
𝑥 𝐹 = 𝑥 𝐺 =.5
𝜎 𝐹,𝐺 = 𝜌 𝐹,𝐺 𝜎 𝐹 𝜎 𝐺 =− =−.09
𝜎 𝑃𝑜𝑟𝑡 2 = .5 2 ∗ ∗ ∗.5∗.5∗ −.09 =0
Since variance is zero, rate of return on portfolio will always be 200*.2=40
𝑟 𝐹 + 𝑟 𝑔 =40
𝟏𝟎+ 𝒓 𝑮 =𝟒𝟎⇒ ⇒ 𝒓 𝑮 =𝟑𝟎