Transcript Document
Test 2 Spring 2014, 10 am Class Multiple Choice #1 Three stocks have annual returns of 8%, 12%, and 16%. The variance of this sample is .𝟎𝟖+.𝟏𝟐+.𝟏𝟔 Average = =. 𝟏𝟐 𝟑 𝟏 Variance = [ . 𝟎𝟖−. 𝟏𝟐 𝟐 + 𝟐 𝟐 . 𝟏𝟐−. 𝟏𝟐 + . 𝟏𝟔−. 𝟏𝟐 ] =. 𝟎𝟎𝟏𝟔 𝟐 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 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 𝑹𝑺 = 𝑹𝒇 + 𝜷 𝑬 𝑹𝑴 − 𝑹𝒇 . 𝟏𝟏 =. 𝟎𝟔 + 𝟐. 𝟓 𝑬 𝑹𝑴 −. 𝟎𝟔 ⟹ 𝑬 𝑹𝑴 =. 𝟎𝟖 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? 𝟏𝟎𝟎 𝟏 𝟕𝟓𝟎 𝑷𝑽 = x 𝟏− + 𝟏𝟎 . 𝟎𝟖 𝟏. 𝟎𝟖 𝟏. 𝟎𝟖𝟗.𝟐𝟓 = $𝟏, 𝟎𝟕𝟖. 𝟗𝟐 𝟑 𝟏. 𝟎𝟖𝟒 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? 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. 𝝈𝑸 = . 𝟎𝟒 =. 𝟐 𝝈𝒁 = . 𝟎𝟗 =.3 Neither 24% nor 30% can be a minimum. 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? 𝟓 𝟏. 𝟎𝟓 𝑷𝑽 = 𝟏− . 𝟐−. 𝟎𝟓 𝟏. 𝟐 = $𝟑𝟓. 𝟓𝟏 𝟔 𝟓 𝟏. 𝟎𝟓 x 𝟏. 𝟐 + .𝟐 𝟔 𝟏 x 𝟏. 𝟐𝟓 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? $𝟏,𝟎𝟎𝟎 𝟏.𝟎𝟗𝟑 Value at 1 pm: = $𝟕𝟕𝟐. 𝟏𝟖 The value decreases by $𝟖𝟎𝟎 − $𝟕𝟕𝟐. 𝟏𝟖 = $𝟐𝟕. 𝟖𝟐 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