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Midterm 2

Midterm 2. SUMMER 2018. Problem 1. A zero-coupon bond will mature in 7¾ years. The bond currently sells for $800, and will pay the bondholder $900 on the date of maturity. What is the effective annual rate of return for this bond? Answer: 1.125 ， R= 1.5314%. Problem 2.

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Midterm 2

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  1. Midterm 2 SUMMER 2018

  2. Problem 1 • A zero-coupon bond will mature in 7¾ years. The bond currently sells for $800, and will pay the bondholder $900 on the date of maturity. What is the effective annual rate of return for this bond? • Answer: 1.125，R= 1.5314%

  3. Problem 2 • An asset that sells for $500 today was worth $400 three years ago. What is the arithmetic average rate of return over this 3-year period? • Answer: • Not enough information to answer. We need to know year-by-year rates to determine arithmetic average.

  4. Problem 3 • Campanili Rock Joe, Inc. will pay its next dividend of $8 later today. Every 12 months, the company will pay a dividend 5% higher than the previous dividend payment. The appropriate effective annual discount rate for this company is 19%. What will the value of the stock be in 2 years, immediately after that day’s dividend payment is made? • Answer: Dividend in 3 years,

  5. Problem 4 • There are 250 stocks available to invest in the fictional East Korea stock market, and risk is measured in standard deviation. Gillian is trying to figure out what the minimum standard deviation could be for a stock portfolio in this stock market. Systematic risk is currently at 20% in this stock market. Unsystematic risk is assumed to be (30/Z)%, with Z denoting the number of stocks in Gillian’s portfolio. What is the minimum standard deviation possible if Gillian can only invest in the East Korea stock market? • Answer: minimum s.d = Systematic risk + minimum unsystematic risk

  6. Problem 5 • A stock’s rates of return over a 7-year period were 6%, –4%, 12%, –50%, –20%, 60%, and 5%. What is the geometric average of the rate of return during this 7-year period? • Answer:

  7. Problem 6 • A US government zero-coupon bond promises a 5% nominal effective annual interest rate, and has one year time to maturity. Inflation is projected to be 8% over the next year. Which of the following must be true if you buy one of these bonds? • Answer: • For real interest rate r, (1+8%)(1+r)=1+5%, r = -2.778%. • The real rate of return for this bond must be negative.

  8. Problem 7 • Assume you have a known distribution of a stock’s rate of return. With 50% probability, the stock will have a 40% rate of return. With 25% probability, the stock will have a 0% rate of return. With 25% probability, the stock will have a –8% rate of return. What is the standard deviation of the stock’s rate of return? • Answer: • The average rate of return will be: • The variance of the returns • S.d.=

  9. Problem 8 • Kadok Krab stock is currently selling for $120 per share. The stock is expected to pay out a $9 annual dividend per year, starting one year from today. What is the internal rate of return for this investment? • Answer:

  10. Problem 9 • Suppose that a moon rock’s current value is $35. With 60% probability, the value of the rock will increase by 10% over the next year. With 40% probability, the value of the rock will decrease by 15% over the next year. What is the probability that a moon rock will have a value over $34 in two years? • Answer: • (up, up): the value of stock = 42.35 >34 • (up, down) or (down, up): the value of stock = 32.725 <34 • (down, down) : the value of stock = 25.2875 <34 • Prob (up, up) = 0.6*0.6 = .36

  11. Problem 10 • A stock’s expected dividend payments will be $1 a year from today, followed by annual payments 20% higher than the previous year. The company is expected to close and pay out its last dividend in 9 years. If these assumptions are correct, and the effective annual discount rate for this stock is 20%, what is the present value of the stock? • Answer: • We cannot use growing annuity formula, since r = g. However, we can see that PV of each payment is: • So PV of 9 dividends payment is *9 = 7.5$

  12. Problem 11 • Use the following information for the next two problems: Love and Happy Honey, Inc. has a known distribution, with a rate of return of 5% two-thirds of the time, and 20% one-third of the time. A risk-free bond has a 7% rate of return. If Love and Happy Honey, Inc. stock has a beta value of 3, what is the market rate of return in the stock market? • Answer: Expected return of stock of return = 5%+*20%=10% =8%

  13. Problem 12 • Use the following information for the next two problems: Love and Happy Honey, Inc. has a known distribution, with a rate of return of 5% two-thirds of the time, and 20% one-third of the time. A risk-free bond has a 7% rate of return. What is the covariance of the rate of return for these two assets? • Answer: • Let Y be risk-free asset. Since for all states of the world, then the covariance with other assets is 0.

  14. Problem 13 • Vienna Vinyl & Vroom, Inc. plans to pay dividends starting 45 months from today. Dividends will be paid every six months, and these payments will continue forever. The first dividend will be $6, and each subsequent dividend will be 5% lower than the previous payment. What is the present value of a share of this stock assuming a stated annual interest rate of 24%, compounded monthly? • Answer: • SAR = 24%, monthly rate = 24%/12 = 2%. • Effective rate for 6 month

  15. Problem 14 • There are three known states of the world, each with one-third probability of occurring: A, B, and C. In state A, stock X has a rate of return of 80% and stock Y has a rate of return of 0%. In state B, stock X has a rate of return of 4% and stock Y has a rate of return of 30%. In state C, stock X has a rate of return of 0% and stock Y has a rate of return of 33%. What is the correlation of Stock X and Y’s rate of return? Remember that all work must be shown to receive credit.

  16. Problem 14 Covariance = (-. 1092+. 0216-.0336)/3= Correlation coefficient =

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