FRM一级练习题(3)答案

FRM一级练习题（3）答案
1. Here the t-reliability factor is used since the population variance is unknown. Since there are 30 observations, the degrees of freedom are 30 – 1 = 29. The t-test is a two-tailed test. So the correct critical t-value is
2.045; thus the 95% confidence interval for the mean return is = [-
3.464%, 11.464%].
2. Assuming the l ong-run estimated variance remains unchanged, the reversion rate defined by the GARCH(1,1) model is (1- - ), which implies that the volatility term structure predicted by the GARCH(1,1) model reverts to the l ong-run estimated variance more sl owly.
3. The cal culation is as foll ows:
Two-thirds of the equity fund is worth USD 40 million. The optimal hedge ratio is given by
h = 0.89 * 0.51 / 0.48 = 0.945
The number of futures contracts is given by
N = 0.945 * 40,000,000 / (910 * 250) = 166.26 c 167, rounded up to nearest integer.
Incorrect:
(A)—This is obtained if you hedge the full portfolio instead of two-thirds.
Incorrect:
(B)—This is obtained if you use the S&P 500 index l evel of 900 instead of the futures price of 910. Incorrect:
(D)—This is obtained if the volatilities of the portfolio and the futures in the formula for the optimal hedge ratio are incorrectly invested.
4. Due to the fact that the American option under consideration is on the stock, which does not pay dividends during the period, its value is equal to the European option with the same parameters. Thus, we can apply the put-call parity to determine the l evel of interest rates.
C – P = S – K e – rT
0.46 – 2.25 = 22 – 24 e – 0.25r
–23.79 = –24e – 0.25r
r = 3.52%
(A) Incorrect answer.
(B) Correct answer.
(C) Incorrect answer: This is obtained if 0.5 year expiration is used instead of three months.
(D) Incorrect answer: Because there are no dividends during the life of the option, put-call parity can be used and the interest rate can indeed be calculated.
5. It is a butterfly spread strategy that can maximize the profit at the target level of USDJPY 97 while limiting the loss to the difference between the premiums of the two long and short calls. Incorrect:
(A)—It is a strad dle strategy suitable for high expected volatility.
Incorrect:
(B)—It is a bull spread strategy suitable for bull expectation on USD.
Incorrect:
(C)—It is a bull spread strategy for USD.
6. The key concept here is the box spread. A box spread with strikes at 120 and 150 gives you a payoff of 30 at expiration irrespective of the spot price. In a sense, it is like a zero coupon bond. Now recall the put-call parity relation:
p + S = c + price of zero coupon bond with face value of strike red eeming at the maturity of the options.
Since the strike is 120, the price of a zero coupon bond with face value of 120 can be expressed as four units of box spread.
If there is any way you can sell any one side of the equation at a price higher than the other there is an arbitrage opportunity.
(A) is correct.
Short one put: +25
Short one spot: +100
Buy one call: –5
Buy six box spreads: –120
Net cash fl ow: 0
At expiry, if spot is greater than 120, call is exercised, and if it is less than 120, put is exercised. In either case you end up buying one spot at 120. This can be used to cl ose the short position. The six spreads will provid e a cash fl ow of 6 * 30 = 180. The net profit is therefore = 180 – 120 = 60.
(B) is incorrect.
Buy one put: –25
Short one spot: +100
Short one call: +5
Buy four box spreads: –80
Net cash fl ow: 0
At expiry, if spot is greater than 120, call is exercised, and if it is less than 120, put is exercised. In either case you end up selling one spot, at 120. However, you are already short one spot, which you have to cl ose. The four box-spreads provide a cash flow of 4 * 30 = 120. The net cash outfl ow = K – S – S – 120 = –2S. You have mad e a loss unless the spot price is zero.
(C) is incorrect. This is exactly the reverse strategy of
(A) And will give you a loss of 60.
(D) is incorrect. You will choose this if you cannot figure out the similarity of the box-spread payoff to that of a zero coupon bond.
7. The cheapest-to-deliver bond on maturity is defined as the one for which the adjusted spot price is the l owest. Adjusted spot price = Spot price/Conversion factor. Computation of adjusted price for each of the bonds is as foll ows:
Bond A = (10214/32)/0.98 = 104.53%
Bond B = (10619/32)/1.03 = 103.49%
Bond C = (9812/32)/0.95 = 103.55%
So, bond B is the cheapest-to-deliver bond, and option (B) is correct.
8.(1) is false. Basis risk can also arise if the underlying asset and hedge asset are id entical. This can happen if
the maturity of hedge contract and delivery date of asset does not match.
(2) is true. Short hedge position or short forward contract benefits from unexpected decline in future prices and consequent strengthening of basis. The payoff to short hedge position is spot price at maturity (S2) and difference between futures price, i.e. (F1 – F2). Thus, payoff = S2 + F1 – F2 = F1 + b2, where b2 is the basis.
(3) is false. Long hedge position benefits from weakening of basis.
(A) is incorrect.
(B) is incorrect.
(C) is correct.
(D) is incorrect.
9.The value of the swap increases / decreases with an increase / decrease in the U.S. five-year fixed rate.
The value of the swap increases / decreases with a d ecrease / increase in the USD-JPY rate.
In
(A), the value of the swap will increase.
(A) is incorrect.
In
(B), the value of the swap will decrease.
(B) is incorrect.
In
(C), the value of the swap will decrease.
(C) is incorrect.
In (D), both factors will cause a decrease in the value of the swap. Hence, (D) is correct.
10. (A) is incorrect. The larger the debt repayments in hard currencies are in relation to export revenues, the greater the probability that the country will have to reschedul e its debt. (B) is incorrect. Since the first use of reserves is to buy vital imports, the greater the ratio of imports to foreign exchange reserves, the higher the probability that the country will have to reschedule its debt repayments. This is the case because the repayment of foreign debt hol ders is generally viewed by countries as being less important than supplying vital goods to the domestic population.
(C) is correct. The investment ratio measures the d egree to which a country is all ocating resources to real investment in factories, machines, and so on, rather than to consumption. The higher this ratio is, the more productive the economy shoul d be in the future and the l ower the probability that the country will need to reschedul e its debt. An opposing view argues for a positive relationship, especially if the country invests heavily in import-competing industries. However, the relationship between the INVR and the probability of rescheduling is most likely to be negative among the four options given.
(D) is incorrect. The more volatile a country's export earnings, the l ess certain creditors can be that at any time in the future it will be abl e to meet its repayment commitments. That is, there should be a positive relationship between VAREX and the probability of rescheduling.
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