Question

estion: A member of an investment committee interested in learning more about fixed-income investment procedures recalls that a fixed-income manager recently stated that derivative instruments could be used to control portfolio duration, saying, “A futures like position can be created in a portfolio by using put and call options on Treasury bonds.”

a. Identify the options market exposure or exposures that create a “futures-like

position” similar to being long Treasury-bond futures. Explain why the position you created is similar to being long Treasury-bond futures.

b. Explain in which direction and why the exposure(s) you identified in part (a) would affect portfolio duration.

c. Assume that a pension plan’s investment policy requires the fixed-income manager to hold portfolio duration within a narrow range. Identify and briefly explain circumstances or transactions in which the use of Treasury-bond futures would be helpful in managing a fixed-income portfolio when duration is constrained.

Short answer

Answer

a. As below

b. Increase duration

c. Offer flexibility to pursue other strategies without worrying about its impact

Step-by-step solution

Step-by-Step Solution

alue at expiration = Value of call + Value of put + Value of stock

= $0 + ($35 – $30) + $30 = $35

Given 5,000 shares, the total net proceeds will be:

(Final Value – Original Investment) × # of shares

Explanation on option market exposure

On buying a call option and writing a put option on a T bond, the total payoff on maturity would be $\left(S_T-X\right)$. This is equivalent to the profit on future’s position with future price X.

If the exercise price (X) is equal to current T-bond future price, the profit on the portfolio would replicate the market traded futures.

Explanation on the direction of the exposure

Just as adding a T-bond would increase the portfolio duration.

Explanation on circumstances

Since the futures can be traded quickly and cheaply, managers get the flexibility to pursue other strategies that don’t affect portfolio duration.