Modifying Portfolio Risk and Return: A Review

"For the most part, there is a $-for-$ relationship between the changes in the price of the underlying security and the price of the corresponding futures contract." Buying futures (taking a long position) increases the exposure to the asset (the return distribution widens), while selling futures (a short position) decreases the portfolio’s exposure (the return distribution narrows). Futures have a symmetrical effect on portfolio returns, "because their impact on the portfolio’s upside and downside return potential is the same." However, options do not have to be exercised, giving the owner the choice. Thus, options DO NOT have a symmetrical effect on portfolio returns. Buying a call option limits losses, buying a put when you are long in the underlying security has the effect of controlling downside risk. Writing a covered call limits upside returns while not affecting loss potential.

Using Derivatives for Asset Allocation

If we expect interest rates to shift quickly, then to take advantage (or to limit our losses), we must quickly shift our portfolio’s assets. However, changes are costly because "securities must be sold and bought to facilitate the re-allocation; attractive securities must be identified for purchase and specific securities in the portfolio must be tagged for sale. Commissions and the market impact of large trades can detract from the portfolio’s return potential." If in a crunch, a PM can use futures rather than identifying specific securities for sale or purchase and rather than issuing large buy/sell orders. Engaging in futures transactions can quickly and easily change a portfolio’s asset mix at lower Tcs. Over time the PM can engage in targeting specific securities, "and do it with a time frame whereby the trading will not have adverse market impacts."

Large portfolios are managed by different individual managers that have areas of specialization. The overall pension fund manager can achieved certain desired effects by engaging in futures transactions, without having to "disrupt the specialized managers by adding or removing large sums of cash from their funds for the purpose of re-allocation."

Using Derivatives to Control Portfolio Cash Flows

Doesn’t matter if your portfolio is actively or passively managed. "In reality, the most frequent use of options to modify portfolio risk is to use options whose underlying ‘security" is another derivative security--a futures contract. These options are called future options or options on futures."

 Hedging Portfolio Cash Inflows:

If a fund manager gets a large influx of cash, the manager, rather that immediately using the funds to purchase securities that he would rather not, can buy bond futures contracts that have a value equal to the deposit. [Purchasing call options is another possibility.] The effect is that the money is immediately invested with lower commissions and less price impact that an outright purchase of bonds. Once the futures have been purchased, the manager has time to make judgment calls on specific bonds. As the bonds are purchased, the futures contracts can be sold.

 Hedging Portfolio Cash Outflows:

A large planned withdrawal is accomplished by selling securities prior to the withdrawal date to generate the cash for the withdrawal. This causes an increase in the cash balance of the portfolio, which reduces the portfolio’s exposure to bonds. [Thus, if Irs decreased after you sold the bonds, but before the cash withdrawal was made, you would lose money over your prior position in the bonds.] The counterbalance the cash increase, you may wish to buy futures contracts or call options as the bonds are sold. "The net effect will be to maintain the portfolio’s overall exposure to bonds while accumulating cash. When the cash is paid out the futures contracts can be sold and the portfolio’s characteristics have not been disrupted."

The Treasury Bond Futures Contract

Futures and options on futures are the derivative tools used most often by portfolio managers. Swaps are also used in PM.

When the T-bond futures contract expires, delivery (or settlement) is made in the underlying security (a T-bond). A T-bond futures contract specifies that the bond that must be delivered is an 8% coupon with at least 15 years to maturity or first call. However, only rarely does such a bond exist! So, why does someone trade a futures contract based on a fictitious underlying asset? Because another T-bond can be substituted for the desired T-bond. If a T-bond with a coupon rate above (below) 8% is delivered, the person accepting delivery pays a higher (lower) price. The seller will deliver the cheapest-to-deliver (CTD) T-bond to satisfy the contract.

 Determining How Many Contracts to Trade to Hedge a Deposit or Withdrawal:

Futures can be used to maintain a desired exposure to bonds while the portfolio receives or disburses cash. To determine the correct # of futures contracts to trade:

The value of 1 contract is the price times $1,000. T-bond futures contracts price quotes are in terms of 32nds. For a quote of 114-26, the price is 114 and 26/32 * 1,000 or $114,812.50. The conversion factor is necessary because the bond to be delivered will probably not be an 8% coupon bond. The conversion factor adjusts the current CTD bond to reflect the fact that it is not an 8% coupon bond. Tables listing the conversion factors for bonds are available from the futures exchanges and many financial institutions.

The duration adjustment factor reflects the difference in interest rate sensitivity between the portfolio and the CTD bond, and is equal to the portfolio duration divided by the CTD duration. [See footnote 19 from Chapter 15 (Investments, 4th edition, by Reilly & Norton).] Caveat: Since we are using durations to find hedge ratios, we are, in effect, assuming that the yield curve is flat, and all yield curve shifts are parallel.

Example:

Assume PM will receive a $5 million cash inflow today and the current conversion factor is 0.90. Our bond portfolio has a duration of 7.5 years and the duration of the CTD bond is 6.5 years. The T-bond futures contract has a price quote of 114-26. [Thus, the dollar value is $114,812.50.] The correct number of T-bond futures to hedge the $5 million cash flow is:

or 45.22 contracts.

Since we can’t buy a fractional number of contracts, the manager will buy 45 contracts to hedge the cash inflow. These 45 contracts will be sold over time as the $5 million in cash is invested in bonds.

NOTE: Throughout the rest of the chapter we will assume no adjustment for a conversion factor is needed.

 Determining How Many Contracts to Trade to Adjust Portfolio Duration:

The duration of a bond portfolio equals the weighted average of the individual component durations. We can buy or sell futures contracts to increase or decrease a portfolio’s duration. This is called the weighted average durations approach. [This is also identical to the BPV method used in Chicago Board of Trade materials.]

Example:

Suppose we have a $25 million portfolio, with $22.5 million invested in bonds and the remaining $2.5 million invested in T-bills. Our portfolio duration is 5.5 years. I expect falling interest rates (and therefore an increase in bond prices). Thus, I would like to increase my portfolio’s duration to , let’s say, 7.5 years. I can do this by adjusting the individual component investments, but I want to do it quickly by trading futures. The price quote of T-bond futures is 114-26 (or $114,812.50), with a duration of 7.0 years. The duration of T-bills is usually assumed to be zero.

Currently the weight of the bond component of our portfolio is:

22.5 million/25 million = 0.90.

The correct number of futures contracts to purchase is represented as F in the following equation:

Solving for F gives us 79.32 contracts must be purchased to increase the portfolio duration to 7.5 years.

If the PM expects a sharp increase in interest rates (and bond prices to drop) and he want to shorten the portfolio duration to 2.0 years, solving for F in the following equation gives us:

-91.76, meaning that 92 contracts must be SOLD to shorten the portfolio duration.

Using Futures in Passive Fixed-Income Portfolio Management

Passive strategies generally follow a buy-and-hold strategy; however, they may try to mimic a bond index. A passive strategy would not involve trying to lengthen or shorten a portfolio’s duration in the light of an expected interest rate increase or decrease. The PM will try to manage deposits and withdrawals without harming the portfolio’s ability to achieve the stated goal. Therefore, the example involving the $5 million cash inflow would be appropriate for a passive strategy.

Using Futures in Active Fixed-Income Portfolio Management

Active management involves adjusting portfolio’s systematic risk, unsystematic risk, or both. Systematic risk = duration, unsystematic risk = portfolio’s exposure due to sector changes or maturity spreads. It is difficult to control a portfolio’s unsystematic risk beyond diversification, but there are well-developed tools to adjust systematic risk.

 Modifying Systematic Risk:

Adjusting the portfolio’s duration allows us to change the portfolio’s exposure to systematic risk (or interest rate risk). If rising interest rates are predicted, we would prefer a shorter duration and vice versa. Traditionally, to accomplish this task, we would engage in the purchase/sale of individual bonds. Futures give managers a quicker and less costly way to accomplish this, with less disruption in the portfolio’s characteristics (which is important, because the active manager may have chosen an undervalued security & not want to sell due to temporary changes in interest rates).

It is possible to sell futures to make your overall portfolio duration unaffected by interest rate changes. [Note, making your portfolio insensitive to IR changes is different from portfolio immunization. PI is a "carefully planned asset allocation strategy wherein the portfolio is constructed to earn a target rate of return that will not be affect by changing interest rates over a known time horizon. PI, if you were hired as an active PM, would be frowned upon by your clients.] Constructing an portfolio that is insensitive to IR changes may be necessary during a period of uncertain or volatile interest rates. We can do this by making our portfolio duration zero. Solving for F in the following equation will give us:

-153.98, or SELL 154 T-bond futures contracts. "By setting the portfolio duration equal to zero, the return earned on the portfolio should approximate those of a risk-free asset such as short-term T-bills.

 Modifying Unsystematic Risk:

"Few opportunities exist for controlling the unsystematic risk in a fixed-income portfolio." "Futures and options exist only in a limited number of broad sectors and maturities. Example of sectors: T-bonds, mortgage-backed securities, and munis. Maturity sectors: Short-term (T-bills, Eurodollars), Intermediate (T-notes), Long-Term (T+-bonds).

"By buying or selling an appropriate number of futures or option contracts, active managers can increase or decrease their portfolio’s exposure to these sectors or yield curve maturities to take advantage of expected sector yield shifts."

Example
Assume a portfolio has a duration of 5 years, which the manager wants to maintain, even though he expects the shape of the yield curve to change (intermediate rates are expected to rise, but long-term rates are expected to fall). To take advantage of the expected change in the yield curve, manager will want to increase exposure in long-term bonds, and decrease exposure in intermediate bonds (and maintain a duration of 5 years). Can do this by selling T-note futures and buying T-bond futures. Because we want the duration to stay at 5 years, the change in interest rate sensitivity must be offsetting, or:

If the value of a T-bond contract is $114,812.50 and the duration is 7 years, and the value of a T-note futures contract is $112,437.50 and the duration is 2.8 years, then:

# of T-notes * $112,437.50 * 2.8 years = # of T-bonds * $114,812.50 * 7.0 years

We can solve for the ratio of T-bond futures contracts to T-note futures contracts: 0.392, which means that for every T-note futures contract sold, 0.392 T-bond futures contracts should be purchased. However, we can not buy or sell fractional amounts, so we must round our purchase of T-bond contracts to the nearest integer. So, if 100 T-note futures contracts were sold, 39 T-bond contracts should be purchased.