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# Time Value of Money & Risk and Return

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1. Discuss the time value of money and its importance. Explain the relationship of discounting and compounding. Suppose you were considering depositing your savings in one of three banks, all of which pay 5 percent interest; bank A compounds annually, bank B compounds semiannually, and bank C compounds daily. Which bank would you choose? Why?

2. Discuss investor's required rate of return, and how the riskiness of an asset is measured and interpreted. Assess how diversifying investments would affect the riskiness and expected rate of return of a portfolio or combination of assets. Discuss unsystematic risk, systematic risk, characteristic line, beta, portfolio beta, and asset allocation.

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This solution discusses the time value of money and investor's rate of return.

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## 25 multiple choice questions on derivatives, international finance, investments

MULTIPLE CHOICE QUESTIONS
1. In a forward contract the party who commits to sell an asset at a specified date in the future takes a(n) position, and the party who commits to buy an asset at a specified date in the future takes a(n) position.
(a) risk seeking; risk averse
(b) open; closed
(c) closed; open
(d) short; long
(e) long; short

2. Assume the one year forward rate for a share of stock is \$45, the spot price is \$41 and the risk free rate is 5% pa. The observed forward price is and the implied forward price is :
(a) \$45; \$41
(b) \$45; \$43.05
(c) \$41; \$45
(d) \$41; \$43.05
(e) \$45; \$38.95

3. An investment strategy that requires no outlay of an investor's own money to generate positive riskless profits is:
(a) arbitrage
(b) risk seeking
(c) portfolio replicating
(e) minimum variance

4. An OTC forward contract is:
(a) an option to call
(b) a forward contract for which the payback is outside the contract period
(c) a customised agreement that is not traded on an exchange
(d) a standardised agreement that is traded on an exchange
(e) a forward contract in which the spot price of the asset at maturity is over the contract forward price

5. The NZ dollar risk free rate is r\$ = 3.0% pa, the euro risk free rate is r? = 7.0% pa, the euro is currently trading at NZ\$2.04 per ?. The implied forward NZ dollar against euro exchange rates at 3 months and at one year are:
(a) NZ\$2.06 per ?; NZ\$2.12 per ?
(b) NZ\$2.12 per ?; NZ\$2.06 per ?
(c) NZ\$2.02 per ?; NZ\$1.96 per ?
(d) NZ\$2.00 per ?; NZ\$1.96 per ?
(e) NZ\$1.96 per ?; NZ\$2.00 per ?

6. A dealer in a commodity is considering a trade in a forward contract. The current spot price of the commodity is \$500 per unit, the forward price for delivery in 1 year is \$540 per unit and the annual inventory costs are 2% of the current spot price. The implied risk free rate is , and the arbitrage profit that could be earned per unit of the commodity in period 1 if the risk-free rate of return is 5% pa in period 0 is .
(a) 4.0%; \$4.20
(b) 5.5%: \$5.09
(c) 5.5%; \$2.70
(d) 6.0%; \$5.00
(e) 6.0%; \$5.40

Questions 7-12 refer to the following information.
Consider a market consisting of only two assets, A and B. There are 100 shares of asset A in the market and the price per share is \$1.00. There are 100 shares of asset B in the market and the price per share is \$2.00.
Asset A has an average rate of return, &#61549;A = 10%.
Asset B has an average rate of return, &#61549;B = 6%.
The risk free interest rate is 5%.
The standard deviation of the market return is 20%.
Assume the market satisfies the CAPM.

7. The asset allocation in the market portfolio is:
(a) &#61559;A = 1/2 ; &#61559;B = 1/2
(b) &#61559;A = 1/4 ; &#61559;B = 3/4
(c) &#61559;A = 3/4 ; &#61559;B = 1/4
(d) &#61559;A = 2/3 ; &#61559;B = 1/3
(e) &#61559;A = 1/3 ; &#61559;B = 2/3

8. The expected return from the market portfolio is:
(a) 7.00%
(b) 7.33%
(c) 8.00%
(d) 8.67%
(e) 9.00%

9. The betas of assets A and B are:
(a) &#61538;A = 1.36 ; &#61538;B = 0.82
(b) &#61538;A = 1.36 ; &#61538;B = 0.27
(c) &#61538;A = 1.15 ; &#61538;B = 0.69
(d) &#61538;A = 1.67 ; &#61538;B = 0.33
(e) &#61538;A = 2.14 ; &#61538;B = 0.43

10. The covariance of the market with asset A is:
(a) 0.0857
(b) 0.0784
(c) 0.0667
(d) 0.0545
(e) 0.0500

11. The equation of the CML is:
(a)
(b)
(c)
(d)
(e)

12. An investment opportunity in the market offers an expected return of 6% with a standard deviation of 19%. If you invested all your money in this opportunity where would your portfolio lie in relation to the CML?
(a) at the point of intersection of the CML and the vertical axis
(b) at the point of intersection of the CML and the horizontal axis
(c) above the CML
(d) below the CML
(e) cannot be determined from the information given

Questions 13-14 refer to the following information.
Consider an economy in which the risk free interest rate is 5%, the return to the market portfolio is 15% and the standard deviation of the return to the market portfolio is 20%.
A firm's shares are currently trading at \$20 per share.
A market analyst reports that the firm's expected dividend is \$2 and it is expected that the share price will remain constant.
Assume the firm's beta is 0.1.

13. What is the expected return from the stock and the stock's risk premium?
(a) 17%; 12%
(b) 25%; 5%
(c) 25%; 20%
(d) 10%; 15%
(e) 10%; 5%

14. What is the risk premium suggested by CAPM? According to CAPM are the firm's shares over-priced or under-priced?
(a) 10%; over-priced
(b) 10%; over-priced
(c) 1%; under-priced
(d) 1%; over-priced
(e) 5%; correctly priced

15. Assume the standard deviation of the market return is 0.2, the standard deviation of asset k is 0.45 and the beta of asset k is 0.675. The correlation coefficient between the return from asset k and the return from the market is:
(a) 0.900
(b) 0.658
(c) 0.444
(d) 0.300
(e) 0.133

16. A portfolio comprises two risky assets. As the correlation between the two assets decreases the standard deviation of the minimum variance portfolio and the standard deviation of the tangency portfolio :
(a) increases; decreases
(b) increases; increases
(c) remains unchanged; decreases
(d) decreases; increases
(e) decreases; decreases

17. A call option is in-the-money if the:
(a) strike price of the option is less than the current price of the underlying asset
(b) strike price of the option is greater than the current price of the underlying asset
(c) strike price of the option is equal to the price of the underlying asset
(d) intrinsic value of the option is zero
(e) settlement date is less than one month from the current date

18. The forward short position with a forward price of E has the same gross return as the combination of which two option positions, each with strike price E?
(a) long call and short put
(b) long put and short call
(c) long call and long put
(d) short put and short call
(e) none of the above

19. The price of a put option as the volatility of the returns of the underlying asset increases, and the price of a put option as the time to expiration decreases.
(a) decreases; remains unchanged
(b) decreases; decreases
(c) increases; increases
(d) increases; remains unchanged
(e) increases; decreases

20. Which of the following statements is NOT true of the Black-Scholes model?
(a) vega is always positive
(b) N(d1) is the &#61540; of the call option
(c) N(d2) is the &#61511; of the put option
(d) the volatility of the underlying asset is the annualised standard deviation of its returns
(e) the volatility of the underlying asset is assumed to be constant

Questions 21-25 refer to the following information.
Assume the current price of a stock is \$43 and the volatility is 0.2. Assume the stock is not expected to pay dividends during the next 6 months. Assume the risk-free interest rate is 10% pa.

21. The Black-Scholes model suggests that the price of a 6 month European call option on the stock where the exercise price of the option is \$40 is:
(a) \$6.29
(b) \$5.56
(c) \$4.83
(d) \$3.72
(e) \$1.86

22. What is the intrinsic value of the call option? What is its the time value?
(a) \$4.00; \$0.35
(b) \$2.72; \$1.00
(c) \$3.00; \$2.56
(d) \$3.00; \$3.29
(e) \$0; \$4.83

23. The probability that the call option expires in-the-money is approximately:
(a) 0.94
(b) 0.83
(c) 0.79
(d) 0.17
(e) 0.06

24. The Black-Scholes model suggests that the price of a 6 month European put option on the stock where the exercise price of the option is \$40 is:
(a) \$0.61
(b) \$0.78
(c) \$0.84
(d) \$1.34
(e) \$2.63

25. The call option is , and the put option is :
(a) in-the-money; at-the-money
(b) out-of-the-money; in-the-money
(c) at-the-money; at-the-money
(d) in-the-money; out-of-the-money
(e) out-of-the-money; at-the-money

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