Using Derivatives in Asset Allocation

Changing Asset Allocation with Futures

Issue:

A portfolio manager in Greece currently manages a portfolio with a 60% allocation to equity and a 40% allocation to fixed income. However, the manager has a bullish outlook on stocks and a bearish outlook on fixed income for the following year. As a result, the manager aims to adjust the portfolio’s allocation to 80% equity and 20% fixed income.

Solution:

The manager can use financial instruments like forwards or futures to achieve the desired allocation. To increase the equity allocation to 80%, the manager can buy forwards or futures on the desired equity index. Simultaneously, to reduce the fixed income exposure to 20%, the manager can sell futures on the bond index. This strategy will allow the manager to make the necessary adjustments to the portfolio’s allocation as per the outlook on the respective asset classes.

The following equation determines the number of equity futures to use:

$$ N_f=\left[\frac {B_T-B_S}{B_f} \right]\left[\frac {S}{F} \right] $$

Where:

\(N_f\) = The number of futures contracts.

\(B_t\) = Target beta of portfolio.

\(B_s\) = Current portfolio beat.

\(B_f\) = Beta of a futures contract.

\(S\) = Size of portfolio ($’ s).

\(F\)= Price of a futures contract.

To calculate the number of fixed-income futures, use the following equation:

$$ BPVHR = \left( \frac {BPV_T – BPV_P }{ BPV_{CTD}} \right) \times CF $$

Where:

\(BPVHR =\) # of contracts to use.

\(BPV_T\) = Basis Point Value (Target).

\(BPV_P\) = Basis Point Value (Current Portfolio).

\(BPV_{CTD}\) = Basis Point Value (Cheapest to Deliver).

\(CF\) = Conversion factor.

Rebalancing an Asset Allocation Using Futures

Issue:

Horace Robertson manages a portfolio with a 50% target allocation in stocks and 50% in bonds. The portfolio value increased from €100 million to €106 million last month. Now, he wants to rebalance it back to the target allocation.

Solution:

To rebalance the portfolio, Robertson will use the formulas above. The exact magnitude of the change in asset classes is unspecified, making it challenging to determine the futures to use and their quantities. However, riskier assets often increase in value and portfolio weight faster than lower-risk assets. Therefore, Grant may sell futures to lower stock exposure and buy index futures to increase bond exposure.

Changing Asset Allocation with Swaps

Swaps can be used to adjust portfolio asset allocation. To increase exposure to a specific asset class, a manager can enter into a swap that receives a return from that asset class. Conversely, the manager can structure the swap so the underlying portfolio pays away exposure to any risk metric they want to reduce. For instance, a manager aiming to reduce risk on the S&P500 and increase exposure to interest rate movement would set up a swap as follows:

Pay: S&P 500 equity return

Receive: Floating LIBOR + 50 Basis Points

Indeed, this layout follows the “start with the big picture” approach but does not provide further details. To determine the size of the swap notional values for each leg, the manager must use the appropriate formula to specify the magnitude and timing of the cash flows.

Inferring Market Expectations

Managers commonly want to develop and express capital market expectations through careful portfolio construction. While not exhaustive, the following are some typical applications of derivatives for inferring market expectations:

1. For predicting FOMC moves: Utilize Fed funds futures.
2. For estimating inflation rates: Employ CPI (inflation) swaps.
3. For gauging market volatility, Refer to VIX futures.

Inferring Expected Average Fed Funds Rate

Investors analyze financial instrument pricing to determine future interest rate outcome probabilities based on central banks' decisions. This indicates how markets are pricing in potential monetary policy changes.

To calculate probabilities of upcoming Fed interest rate actions, look at the pricing of Fed funds futures. These futures are tied to the adequate federal funds (FFE) rate, not the Fed's target rate.

Fed funds futures contract price = 100 – Expected FFE rate.

The probability of a change in rates is often estimated by analyzing current market data with the help of the following formula:

Effective fed funds rate implied by futures – Current fed funds rate

Fed funds rate assuming a rate hike – Current fed funds rate

Adam Marboro manages a portfolio of short-term floating-rate corporate bonds. At the upcoming meeting, he wants to know the market's expectations for potential Federal Reserve rate actions. Marboro observes that the current price for the Fed funds futures contract, expiring after the next FOMC meeting, is 97.80. The current federal funds rate target range is between 1.75% and 2.00%. Let's demonstrate how Marboro can use this information to determine the following:

The expected average FFE rate:

The FFE rate implied by the futures contract price is 2.2% (calculated as 100 – 97.80). The manager understands that this is the rate market participants expect to be that month’s average federal funds rate.

Question

Managers who wish to infer expectations for inflation rates would most appropriately use which of the following?

1. Fed funds futures.
2. CPI swaps.
3. VIX futures.

Solution

The correct answer is B.

A CPI swap is a derivative instrument that allows one party to exchange a fixed rate of interest for a floating rate linked to the Consumer Price Index (CPI), which is a measure of inflation. By using CPI swaps, managers can hedge against inflation risk or speculate on inflation expectations.

A is incorrect. Fed funds futures are contracts that allow investors to bet on the future level of the federal funds rate, which is the interest rate that banks charge each other for overnight loan. The federal funds rate is influenced by the monetary policy of the Federal Reserve, which targets a certain level of inflation. However, the federal funds rate is not a direct measure of inflation expectations, and may diverge from them depending on the economic conditions and the Fed’s actions.

C is incorrect. VIX futures are contracts that allow investors to trade the expected volatility of the S&P 500 index, based on the Cboe Volatility Index (VIX) methodology. The VIX index reflects the market’s estimate of the future volatility of the S&P 500 index, which is influenced by various factors such as earnings, news, sentiment, and uncertainty. The VIX index is not a measure of inflation expectations and may have a positive or negative correlation with them depending on the market environment.

Derivatives and Risk Management: Learning Module 2: Swaps, Forwards, and Futures Strategies; Los 2(f) Demonstrate the use of derivatives in asset allocation, rebalancing, and inferring market expectations