Risk Latte - FRM 04 Quiz # 7

The bid-ask spread of a highly illiquid asset is 150 basis point. A fund manger has $1 million in this asset whose daily volatility is 1%. Therefore, the liquidity adjusted 95% one Day VaR of this asset would be:

a) $15,850.
b) $17,290
c) $18,525
d) $23,950.

A Forward Rate Agreement (FRA) can be decomposed into:

a) A long 6-,month T bill and a short 12-month T bill.
b) A short 6-month T bill and a long 12-month T bill.
c) A long 6-month T bill and a long 12-month T bill.
d) A long 12 month bond with 6 month semi-annual coupons.

A trader is ling 6 X 12 FRA. Therefore, his position is equivalent to:

a) A long 6-month T bill and a short 12-month T bill.
b) A short 6-month T bill and a long 12-month T bill
c) A long 6-month T bill and a long 12 month T bill
d) A long 12 month bond with 6 month semi-annual coupons.

Suppose a trader sells a 6 X 12 FRA on $100 million. The current of 6 month zero coupon rate is 5.63% and the daily volatility of a 6 month zero is 0.16% and that of a 12 month zero is 0.47%. The correlation between the 6 month zero and the 12 month zero is 0.65. The one standard deviation daily VaR the position is:

a) $275,450.
b) $350,000
c) $418,510
d) $573,004

Nikkei225 index (futures) is trading at 12,000. A trader is short 10,000 3-month ATM calls and 10,000 3-month ATM puts on the Nikkei225 (short straddle position). The current implied volatility of Nikkei is 13%. Assume a Yen interest rate of zero and USD/JPY FX rate of 100. It the multiplier on the Nikkei225 index is 500 Yen for the options contract then the 95% 1-month VaR of the straddle using delta would be:

a) Zero
b) $85,000.
c) $125,000
d) $350,000

In the previous question the 95% 1-month VaR of the straddle using delta-gamma approximation would be:

a) $1.65 million;
b) $4.35 million
c) $8.32 million
d) $12.07 million

The skewness coefficient of a normal distribution (for an asset return) is -2.83. Hence, using Cornish-Fisher transformation the corrected value of alpha, the standard normal deviate, for 95 % confidence interval would be:

a) 1.98
b) 2.05
c) 2.45
d) 3.15

A bond fund manager wants to hedge a fixed income portfolio which has a duration of 8.65 by allocation funds to two zero coupon bonds in such a way that weighted duration of the two bonds should match the duration of the portfolio. If the first zero coupon bond matures in 5 years and the second one matures in 10 years, then what proportion of the funds should the manager allocate to the two bonds:

a) 27% of the funds to the first bond and the rest to the second bond.
b) 33% of the funds to the first bond and the rest to the second bond.
c) 47% of the funds to the first bond and the rest to the second bond.
d) 63% of the funds to the first bond and the rest to the second bond.

The spot FX trading desk of a bank has two star traders, one of whom trades a G7 currency which has an annualized volatility of 9% and the other who trades a highly illiquid emerging market currency which has an annualized volatility of 18%. The G7 trader has an exposure of $150 million and has made a profit of $10 million on it. The emerging markets trader has an exposure of $100 million and has also turned in a profit of $10 million. The treasury of the bank rewards all traders according to the risk adjusted return on capital methodology. Therefore, the trader who gets the higher bonus would be:

a) the G7 trader
b) the emerging markets trader
c) both the traders should get identical bonuses.
d) The bonus cannot be determined from the above information

If the treasury of the bank has a policy to hold enough capital to cover 99% of all FX losses, the bonus of the risk adjusted return(RAROC) of the G7 trader will be:

a) 12.50%
b) 23.45%
c) 31.79%
d) 43.12%