Delsing should sell stock index futures contracts and buy bond futures
This strategy is justified because buying the bond futures and
selling the stock index futures provides the same exposure as buying the
bonds and selling the stocks.
This strategy assumes high correlation between
the bond futures and the bond portfolio, as well as high correlation between
the stock index futures and the stock portfolio.
The number of contracts in each case is:
5 × $200,000,000 × 0.0001 = $100,000
$100,000/97.85 = 1022 contracts
$200,000,000/($1,378 × 250) = 581 contracts
The market value of the portfolio to be hedged is $20 million.
market value of the bonds controlled by one futures contract is $63,330.
If we were
to equate the market values of the portfolio and the futures contract, we would sell:
$20,000,000/$63,330 = 315.806 contracts
However, we must adjust this “naive” hedge for the price volatility of the bond
portfolio relative to the futures contract.
Price volatilities differ according to both the
duration and the yield volatility of the bonds.
In this case, the yield volatilities may
be assumed equal, because any yield spread between the Treasury portfolio and the
Treasury bond underlying the futures contract is likely to be stable.
duration of the Treasury portfolio is less than that of the futures contract.
the naive hedge for relative duration and relative yield volatility, we obtain the
adjusted hedge position:
Here, the treasurer seeks to hedge the purchase price of the bonds; this
requires a long hedge.
The market value of the bonds to be purchased is:
0.93 = $18.6 million
The duration ratio is 7.2/8.0, and the relative yield volatility is 1.25.
hedge requires the treasurer to take a long position in: