Practice problems guidelines for revision, FM&I
1.
2.
3.
4.
5.
Calculation of spot rates and forward rates (C3)
Calculation of T-Bill prices, discount level and annualized yield (C6)
Calculation of bond price, YTM, duration and convexity (C8)
Calculation of futures payoff (C13)
Calculation of options payoff/profit/moneyness (C14)
1. Current market rate is 6.2%/year for one year loans, you predict that this rate is kept constant
for the next 4 years and rise by 30bps in year 5. If you believe in expectation theory, what can
you say about modified duration of a bond assuming similar risk, with term to maturity of 5
years, 6% annual coupon rate?
ANS: Use PET to get 5 year rate, 0.0625956.
Use this rate to find MDUR of bond 4.199 (DUR = 4.46)
2. Current market rate is 9.3%/year for one year loans, you predict that this rate is kept constant
for the next 3 years and go down by 30bps in year 4 and kept stable onward. If you believe in
expectation theory, what can you say about current 5 year rate and the shape of the yield curve?
ANS: Use PET to get 5 year rate, 9.18%.
According to the figures, yield curve should be downward sloping
3. You have just taken a long put European option on FTU share with a strike price of 31.200
VND/share. The size of each contract is 100 units and you have 20 contracts. This contract is
bound to expire on Dec/2017.
a. If FTU is now priced at 30,000 VND, do you exercise your contract, and why?
b. If on the closing day, FTU is priced at 33,000 VND, what shall be your profit from the contract,
knowing that the premium for the option is 200VND/share?
ANS: Since position is LP
a
b
S0 < K: LP in the $, excercise if type is American, not if European
St>K, LP out of the $, lose premium paid
200*100*20
=400,000
4. You have just taken a long call European option on FTU share with a strike price of 31.200
VND/share. The size of each contract is 100 units and you have 20 contracts. This contract is
bound to expire on Dec/2017.
a. If FTU is now priced at 30,000 VND, do you exercise your contract, and why?
b. If on the closing day, FTU is priced at 33,000 VND, what shall be your profit from the contract,
knowing that the premium for the option is 200VND/share?
ANS: Since position is LC
a. S0<K, LC is out of the $, do not excercise
b. St>K, LC is in the $, exercise and get (33,000-31,200-200)*100*20 = 3,200,000
5. You have just bought a 10,000$ par value, 6 month (180days) T-Bill, the current market rate is
6.6%/year. After 30 days, this T-Bill sees a drop in market rate to 5.8%/year. Calculate your
profit/loss for this period?
ANS: Find two prices, keeping in mind that after 30 days new price must reflect new maturity.
P1 = 9680.54
P2 = 9764.04
Profit = 83.5
6. What can you say about convexity of a bond, with term to maturity of 8 years, 8% annual
coupon rate and YTM of 7.2%? If new market rate for similar bond is adjusted to 7%, what is
your expectation of bond price change using convexity estimation?
ANS:
Convexity: 44.70, (MDur: 5.83)
Estimated price adjustment: 1.18%