1. Test 2
Spring 2014, 10 am Class

2. Multiple Choice #1
Three stocks have annual returns of 8%, 12%, and 16%. The variance of this sample is Average = .𝟎𝟖+.𝟏𝟐+.𝟏𝟔 𝟑 =.𝟏𝟐 Variance = 𝟏 𝟐 [ .𝟎𝟖−.𝟏𝟐 𝟐 + .𝟏𝟐−.𝟏𝟐 𝟐 + .𝟏𝟔−.𝟏𝟐 𝟐 ]=.𝟎𝟎𝟏𝟔

3. Multiple Choice #2
Amy invested $1 in a company 50 years ago. This investment is worth $60 today. What is the geometric average annual return on this investment? Geometric Average = 𝟓𝟎 𝟔𝟎 −𝟏=.𝟎𝟖𝟓𝟑𝟑𝟑

4. Multiple Choice #3
Assume that the risk-free return in the market is currently 6%, and that a stock with 𝛽 of 2.5 has an expected return of 11%. What is the expected return on the market portfolio (as defined in lecture)? 𝑬 𝑹 𝑺 = 𝑹 𝒇 +𝜷 𝑬 𝑹 𝑴 − 𝑹 𝒇 .𝟏𝟏=.𝟎𝟔+𝟐.𝟓 𝑬 𝑹 𝑴 −.𝟎𝟔 ⟹𝑬 𝑹 𝑴 =.𝟎𝟖

5. Multiple Choice #4
Bo’s Buckwheat and Barley, Inc. has issued a bond with 10 remaining coupon payments of $100 each. The first will be paid in 3 months, and each subsequent payment will be made annually. The bond also pays out a face value of $750 with the last coupon payment. If the effective annual discount rate is 8%, what is the present value of the bond? 𝑷𝑽= 𝟏.𝟎𝟖 𝟑 𝟒 x 𝟏𝟎𝟎 .𝟎𝟖 𝟏− 𝟏 𝟏.𝟎𝟖 𝟏𝟎 + 𝟕𝟓𝟎 𝟏.𝟎𝟖 𝟗.𝟐𝟓 =$𝟏,𝟎𝟕𝟖.𝟗𝟐

6. Multiple Choice #5
Stock Q has an expected return of 8% and a variance of .04. Stock Z has an expected return of 14% and a variance of .09. The correlation is strictly greater than -1 and strictly less than 1. Which of the following – 8%, 16%, 24% 32% – could NOT be the standard deviation at the minimum variance point of a portfolio consisting of Stock A and/or B?

7. Multiple Choice #5
Since 𝜌≠1, the minimum standard deviation of a portfolio mixing the two stocks must be below the standard deviation of both stocks. 𝝈 𝑸 = .𝟎𝟒 =.𝟐 𝝈 𝒁 = .𝟎𝟗 =.3 Neither 24% nor 30% can be a minimum.

8. Free Response #6
Charlotte buys a stock that pays a dividend of $5 today (May 28, 2014), followed by annual dividends on the same date each year forever. The dividends grow by 5% each year until 2020 and then remain constant forever. If the effective annual discount rate is 20%, what is the present value of the stock?
𝑷𝑽= 𝟓 .𝟐−.𝟎𝟓 𝟏− 𝟏.𝟎𝟓 𝟏.𝟐 𝟔 x 𝟏.𝟐 + 𝟓 𝟏.𝟎𝟓 𝟔 .𝟐 x 𝟏 𝟏.𝟐 𝟓
=$𝟑𝟓.𝟓𝟏

9. Free Response #7
A zero-coupon bond is purchased for $800 at 10 am today, with a face value of $1,000 to be paid 3 years from today. Later today, at 1 pm, the yield to maturity (as an effective annual rate) changes to 9%. How much does the value of the bond change between 10 am and 1 pm?
Value at 1 pm: $𝟏,𝟎𝟎𝟎 𝟏.𝟎𝟗 𝟑 =$𝟕𝟕𝟐.𝟏𝟖
The value decreases by $𝟖𝟎𝟎−$𝟕𝟕𝟐.𝟏𝟖=$𝟐𝟕.𝟖𝟐

10. Free Response #8
A sample of a stock’s returns over the past 5 years was 200%, 50%, -40%, 20%, and -10%. If the stock is worth $200 per share today, how much would each share have been worth 5 years ago? 𝑿 𝟏+𝟐 𝟏+.𝟓 𝟏−.𝟒 𝟏+.𝟐 𝟏−.𝟏 =$𝟐𝟎𝟎 𝑿=$𝟔𝟖.𝟓𝟗