21 Jun WHY DOES A CALLABLE BOND EXHIBIT NEGATIVE CONVEXITY?
Consider the following probability distribution for stocks A and B for questions 1 and 2
STATE Probability Return on Stock A Return on Stock B
1 0.10 10% 8%
2 0.30 20% 12%
3 0.60 25% 17%
Calculate the Expected return for Stock A and for Stock B
2. Using the same table above, calculate the variance for both Stock A and for Stock B.
3. For a portfolio that contained just two stocks, what would be the preferred correlation coefficient between the two stocks? Explain.
4. As the number of securities in a portfolio is increased, what happens to the average standard deviation of the portfolio?
5. You have an opinion that CSCO has an expected return of 0.1375. The stock has a beta of 1.3. The risk free rate is .04 and the market expected rate of return is 0.115. According to the CAPM, is this security OVERPRICED, UNDERPRICED or FAIRLY PRICED?
6. Tell me in your own words, the meaning of VAR (Value at Risk). How can an investor use this tool when evaluating an investment portfolio?
7. You purchase one JNJ call option with a strike price of $75 for a premium of $3.Ignoring transaction costs, what is the break-even of this position; Conversely, you write one ATT put option with a strike price of $50 for a premium of $5. What is the break-even of this position?
8. On April 1, you shorted one S&P 500 futures contract at a futures price of $1,550. If, on June 15, the futures price was $1,612, what would be your profit or loss if you closed your position?
9. Talk to me about how an investor can “hedge” a long position on Treasury bonds.
10. Describe in your own words the meaning of DURATION and how Duration is a measure of interest rate sensitivity?
11. Why do investors like CONVEXITY when managing bonds?
12. Describe the price and yield curve changes for a callable bond? Why does a callable bond exhibit negative convexity?
13. Which one of the following bonds is more price sensitive to changes in interest rates and why?
a. Exxon 10% coupon due in 12/31/2022 selling at $100
b. USTN 0% due in 12/31/2022with a yield of 10% (this is a zero coupon bond)
14. An Apple bond has a duration of 6. If yields increase by 1%, what will be the effect on the bond’s price
15. If an investor desires a bond with a lower duration, holding other factors constant
a. Should he choose a HIGHER or LOWER coupon?
b. Should he choose a SHORTER or LONGER maturity?
c. Should he choose a HIGHER or LOWER yield to maturity?
16. If a bond manager expects the yield curve to sharply steepen with longer rates going higher and shorter rates going lower, what type of duration would the manager prefer? Which of the following bonds would best accommodate the manager under this scenario?
a. ATT 12% due 12/31/2017 @ 10% yield
b. DuPONT 3% due 12/31/2047 @ 10% yield
c. USTN 3% due 12/31/2047 @ 6% yield
17. Calculate the duration of the following bond: 1,000 JNJ 6% due 12/31/2019 with a yield of 4%.
18. Consider a bond with a 30 maturity, an 8% coupon, and a yield of 8%. The duration of this bond is 11.26 and the convexity is 212.4. If the bond’s yield increases from 8% to 11%, tell me how the price of the bond will change
19. When evaluating between two different mutual funds, discuss how an investor can use the Sharpe Ratio and the Treynor Ratio to determine which fund is most appropriate.
20. You are an investor who has just retired after 45 years in the work place. Up until now, your investment portfolio consisted of low –yielding and high risk growth stocks. However, as medical costs continue to rise and you need to supplement your Social security with more monthly income, discuss some changes to this investor’s portfolio to meet his need for higher income.
21. Explain how an investor can add “Alternative Investments” such as Private Equity or Hedge Funds to increase the risk-adjusted return of a portfolio.
22. From our discussions in class, we stressed the idea of managing the risk of an investment portfolio. How can an investor QUANTIFY the risk of a portfolio? How can an investor assign a NUMBER to this risk
23. Compare and contrast the investment portfolio of two very different investors. The first is an individual who has just entered the workforce with a 50 year time horizon ahead of him; the second is a 60 year-old man who plans to retire in 5 years. Talk to me about the differences in their asset allocation and how both can manage risk.
24. Consider an multi-million dollar endowment fund of a university that is required to pay out 5% of their market value every year to deserving students in the form of a scholarship. Thus, the university must make this 5% distribution in periods of strong as well as weak market returns. Talk to me about the risks of this investment portfolio and how the investment manager can manage this risk.
25. Throughout this block, we discussed various measures of quantifiable risk including Standard Deviation, Beta and VAR. How can an investor use each of these measures when managing their own investment portfolio?
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