8006 Reviews Questions

When hedging an equity portfolio with index futures, the number of futures contracts to hold is given by the [beta x value of portfolio/value of one futures contract]. Therefore Choice 'a' is the correct answer.

The volatility, risk free rate have nothing to do with determining the number of futures contracts to hold. Systematic risk is expressed in the form of beta. Therefore the other choices are incorrect.

The put-call parity can be expressed as:

Call – Put = Spot – PV of exercise price

Note that a negative sign above means a short position. The 'term PV of exercise price' is the same as a bank deposit placed today equivalent to the PV of the exercise price so that we will have the cash flow on the exercise date to exercise the option.

Therefore only Choice 'd' is the correct answer as rearranging the above gives us Buying a call + Bank Deposit = Buying the stock + Buying a put.

Choice 'd' is therefore the correct answer.

The underlying asset in a treasury bond futures contract is any long term US Treasury bond with a maturity of more than 15 years and not callable within 15 years. The underlying asset in a Treasury note futures contract is any long term Treasury note with a maturity of no less than 6.5 years and no more than 10 years.

Note the difference between what the underlying asset is for treasury bond futures and treasury note futures. In either case, adjustments will be made for the coupon and maturity of the actual bond delivered (the concept of the adjustment of 'cheapest-to-deliver').

Since the 10 year rate has stayed the same, but the curve has gone from being flat to upward sloping, it means the shorter term interest rates have gone down. Recall that Macaulay duration is the PV of the payments received on a bond over its life weighted by the year each payment is received in. Also remember that a bond's current price is nothing but the summation of the different PVs of its various payments. It effectively gives the real average life of the bond - for example if a hypothetical (and impossible) bond derives half of its value from a payment today and the other half from a payment in 10 years, the investor can look at the average as being 5 years (0*50% + 10*50%). That is what is what we are calculating when deriving Macaulay duration.

In this case, a reduction in the near term interest rates increases the PV of the payments received prior to the payment at 10 years. This increases the value of the bond, and also increases the weightage of the earlier payments, decreasing the Macaulay duration (by shifting it closer to now and further behind from the maturity date).