Question

Interest Rate Option

As portfolio manager for the Fredericks Fund, you are increasingly interested in making “Macro Bets”. That is using whatever tools are available to develop strategies that profit from Macro Economic conditions changing as you anticipate.
It is March of 2018, and you are interested in utilizing Interest Rate Options, options where the underlying is an interest rate, in directional bets, or volatility bets. After listening to the Federal Reserve news conference on the money supply, interest rates, and Fed Policy, you are convinced the Federal Reserve will be aggressive this year in raising interest rates. You believe there will be at least four increases to the target Fed Funds Rate.
You ask your assistant manager to collect option premium data for the December 2018 expiration. He shows you the following data:
CBOT Interest Rate Options FVX – US Treasury 5 Year Maturity December 2018 Expiration as of March 2018

  i Strike i x 10 CALLS PUTS

2.60% 26.00       4.68         0.00        

2.65% 26.50       4.19         0.01       

2.70% 27.00       3.71         0.01       

2.75% 27.50       3.24         0.03        

2.80% 28.00       2.78         0.06        

2.85% 28.50       2.34         0.11        

2.90% 29.00       1.93         0.18        

2.95% 29.50       1.55         0.29        

3.00% 30.00       1.22         0.44        

3.05% 30.50       0.93         0.64        

3.10% 31.00       0.69         0.88        

3.15% 31.50       0.49         1.17        

3.20% 32.00       0.34         1.51        

3.25% 32.50       0.23         1.89        

3.30% 33.00       0.15         2.29   T = 0.75 r = .035 ? = .075

  Currently, the five-year note is trading around 2.75 – 2.85. Your scenarios are for rates to go at least to 3.10 – 3.15. Your most optimistic scenario is 3.30 – 3.50. Worst case the Fed does nothing.
A. Create a “Bullish” directional strategy utilizing the listed options. Utilize a short option to finance your long position. B. Calculate the net cost and profit assuming rates move to 3.10 – 3.15. C. Show your strategy on a payoff graph. Label the points that comprise strike and break-even points.

Answer 1

A)

As from the question we take strike price as given in table and at that point we go long for increase in interest rate and short for decrease in interest rate.

i.e. we get by selling call and and buy from that our put.

Here for bullish strategy we will be selling call options at current interest rate as a strike price and buying from the proceeds the put options (long). So as the interest rate increase happens put price increases and call price decreases.

B)

Suppose the strike interest rate for both put and call option is 2.75%

So from the table by selling one call option we will have $3.24 from which we can buy 108 put options (Neglecting transcation cost)

= 3.24 / 0.03 = 108

Now if interest rate goes to 3.1% than call option expires worthless and put option have price = 0.88

So the payoff will be=

= (0.88 - 0.03) * 108

= $91.8

If the interest rate goes to 3.15% than put option price will be $1.17 and payoff will be =

= (1.17 - 0.03) * 108

= $123.12

So our benefit will be between $91.8 - $123.12.

C)

For the worst case when Fed does not change the interest rate and if we have strike interest rate more than present interest rate in this case we will have a loss as our put option will go worthless and we have to pay for call selling.

So i am only taking strike rate as the current interest rate which is between 2.75-2.85

So in worst case we will not have any loss and profit (Neglecting transaction cost).

For strike rate 2.75% payoff will be caculated as below:-

= Payoff = (Final Price - Bought Price ) * Total No. of options bought

for 2.75% rate we bought 108 put options ( 3.24 / 0.03)

so

= Payoff = (Final Price - Bought Price ) * 108

Please refer below table and graph for payoff

i strike	Call	Put	Payoff for 2.75%
2.75	3.24	0.03	0
2.8	2.78	0.06	3.24
2.85	2.34	0.11	8.64
2.9	1.93	0.18	16.2
2.95	1.55	0.29	28.08
3	1.22	0.44	44.28
3.05	0.93	0.64	65.88
3.1	0.69	0.88	91.8
3.15	0.49	1.17	123.12
3.2	0.34	1.51	159.84
3.25	0.23	1.89	200.88
3.3	0.15	2.29	244.08

Now for Strike rate 2.8%:-

Total no. of put options bought = 2.78 / 0.06 = 46 approx

So payoff has been calculated with the same above formula and table with graph is resulted as below:-

i strike	Call	Put	Payoff for 2.8%
2.8	2.78	0.06	0
2.85	2.34	0.11	2.3
2.9	1.93	0.18	5.52
2.95	1.55	0.29	10.58
3	1.22	0.44	17.48
3.05	0.93	0.64	26.68
3.1	0.69	0.88	37.72
3.15	0.49	1.17	51.06
3.2	0.34	1.51	66.7
3.25	0.23	1.89	84.18
3.3	0.15	2.29	102.58

Now for Strike rate 2.85%:-

No. of put options bought = 2.34 / 0.11 = 21 approx

So payoff table and graph is

i strike	Call	Put	Payoff for 2.85%
2.85	2.34	0.11	0
2.9	1.93	0.18	1.47
2.95	1.55	0.29	3.78
3	1.22	0.44	6.93
3.05	0.93	0.64	11.13
3.1	0.69	0.88	16.17
3.15	0.49	1.17	22.26
3.2	0.34	1.51	29.4
3.25	0.23	1.89	37.38
3.3	0.15	2.29	45.78

Here break even point will not occur as the break even point will come we our losses due to call option and profit due to put option equalizes each other. As we took strike rate at the money break even will not occur here as per given conditions.

However if we increase the strike rate more than 2.85% break even point will occur but as you can see by increasing the strike rate we are decreasing our profit so after the break even point our losses will overcome our profit (Less profit more losses).

Thank You!!