Investing Guide

Individuals may sometime need to change the systematic (beta) exposure of their portfolio.  One can use futures to adjust the Beta of a portfolio.  The formula to determine the number of futures contracts needed is:

Number of futures position = (Beta target - Beta of Portfolio) * Market value of Portfolio / Price of futures contract

If an investor had a 1 million dollar portfolio with 60% stocks index and 40% bond and wanted to convert their allocation to 50/50 stocks and bond, they would need to convert 100,000 of their stock position to cash by shorting the appropriate amount of stock index futures.

Let’s say the stock index futures contract price is 2,500 with a beta of 1.  The stock portfolio has a beta of 0.85.  Using the formula:

(0 - .85)/1 * 100,000/2,500 = -34 contracts.  In order to convert the 100,000 portion of the stock index to cash, we would need to short 34 stock index futures.  With the synthetic cash, we will now convert the cash into the bond position by going long on a bond index futures.

The formula for calculating the number of bond futures to essentially the same as the stock index formula except we replace beta with modified duration.

(Modified duration Target - Modified Duration Portfolio) * Mv of Bond/ future price

If the modified duration of the portfolio = 6, bond index duration = 7, bond index price is 1,250, we can now figure out how many bond futures position to go long.

(6 - 0)/7 *100,000/1,250 = 68.57.  The 100,000 has a duration of zero because it is the synthetic cash that we converted from the stock portfolio.

Using futures may be a cheaper alternative than buying and selling positions, especially if an investor does not want to delay capital gains taxes.  Investors can choose to hold cash and create a synthetic stock position by going long futures if liquidity is a concern.  Using futures may be a good use for someone employing tactical asset allocation.

Companies usually immunize their liabilities by matching duration or cash flow. 

If duration of the portfolio < liability duration, there will be reinvestment risk-the risk of losing money when interest rates fall because the price increase will be less than the reinvested coupons.

If duration of the portfolio > liability duration, there will be price risk-the risk that the loss of principal when interest rates rise because the loss in price is more than the gain on the reinvested coupons.

Duration changes when interest rates fluctuate and as time passes.  One must weigh the transaction costs with the benefits of rebalancing a portfolio.

To avoid immunization risk (assets and liabilities changes do not match) portfolio managers can try to minimize cash flow dispersion around the maturity date by using bullets and barbell strategies.