Overseeing Risk Related to Equity

Equity Swaps

Equity swaps provide an attractive solution for portfolio managers seeking to adjust their equity exposure. These swaps offer a quick, cost-effective, and efficient method to achieve the desired changes. Portfolio exposure to equities is commonly assessed using portfolio beta. When aiming for reduced equity exposure, managers can lower their portfolio beta by exchanging the return on an equity index for an alternative return.

On the other hand, managers looking to increase their beta exposure can exchange a different return (such as interest rate or another index return) for the desired index return. Various variations of equity swaps exist, including scenarios where managers receive equity return and pay fixed, receive equity return and pay floating, or receive equity return and pay another equity return. These variations cater to different objectives and strategies of portfolio managers.

Example

An institutional investor with a $10 million portfolio of UK stocks indexed to the FTSE anticipates a decline in the index over the next six months. To reduce his market exposure by 10%, he entered an equity swap with a notional principal of $1 million. In this swap, he agrees to pay the return on the index and receive LIBOR of 2.75% minus 25 bps, resulting in a net annual rate of 2.50%.

The investor expects the equity market to decline. So, the crucial question is whether they would exchange the equity index return for something else or receive an alternative return in exchange for the equity index return. Analyzing the directional exposure is essential in this case.

Scenario 1 (Equity market increases by 8%)

The investor, who has agreed to pay the return on the index, will experience a negative exposure to the market. When the equity market increases by 8%, the manager will need to pay:

$$
\$10,000,000 \times 10\% \times 8\% = \$80,000; \text{ representing a loss of } \$80,000. $$

The manager will receive:

$$
\$10,000,000 \times 10\% \times 2.5\% \times \frac{180}{360} = \$12,500. $$

Total swap exchange would be:

Pay $80,000 and receive $12,500, net payment (loss on swap position) of $67,500.

Scenario 1 (Equity market decreases by 8%)

The manager will need to pay:

$$
\$10,000,000 \times 10\% \times -8\% = -\$80,000 $$

The manager will receive:

$$
\$10,000,000 \times 10\% \times 2.5\% \times \frac {180}{360} = \$12,500. $$

Total swap exchange would be:

Pay -$80,000 and receive $12,500, net receipt (gain on swap position) of $92,500.

The cash flows illustrate that the portfolio manager has taken a short position in the equity market by agreeing to pay the return on the market in exchange for a fixed interest rate. This is evident from the receipt of funds when the equity index declines.

Equity Forwards and Futures

Equity forwards and futures work in essentially the same manner as the swap. However, there are differences in their trading characteristics. Equity forwards are traded over-the-counter (OTC) and are not regulated, while equity futures are standardized and traded on regulated exchanges. Due to the standardization of futures contracts, managers must calculate the required number of contracts to adjust portfolio exposure. The following equation, with some variations based on context, is commonly used in the CFA curriculum, particularly for equity futures:

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

Where:

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

\(B_t\) = Target beta of the portfolio.

\(B_s\) = Current portfolio beat.

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

\(S\) = Size of the portfolio ($’ s).

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

Negative \(N_f\) values indicate selling or shorting futures contracts, reflecting a bearish outlook. Conversely, positive \(N_f\) values indicate buying or going long on the contracts, reflecting a bullish outlook.

Note that if the investor intends to raise the portfolio's beta, \(\beta_T\) will surpass \(\beta_S\), resulting in a positive value for \(N_f\). This indicates the necessity to purchase futures contracts. Conversely, if she aims to decrease the beta, \(\beta_T\) will be less than \(\beta_S\), leading to a negative value for \(N_f\), necessitating the sale of futures contracts. This relationship should be intuitively clear: Selling futures contracts mitigates some risk associated with holding the stock, while buying futures contracts introduces additional risk. In the unique scenario where the objective is to eliminate market risk, \(\beta_T\) would be set to zero, leading to the following simplified formula:

$$
N_f=-\left[\frac {\beta_s}{\beta_f} \right]\left[ \frac {S}{F} \right] $$

In this scenario, \(N_f\) will consistently have a negative sign, which aligns with the rationale that, to mitigate market risk fully, it is necessary to engage in the selling of futures contracts.

Cash Equitization

Cash securitization, called “cash equitization” or “cash overlay,” aims to enhance returns by optimizing unintentional cash holdings. This strategy involves fund managers acquiring futures contracts to mimic the performance of the underlying market where the cash would have been invested.

Leveraging the liquidity of the futures market makes this approach relatively straightforward. Another option is to buy call options and sell put options on the underlying asset, having the same exercise price and expiration date.

With a cash holding indicating \(\beta_S = 0\), the quantity of futures contracts (with a beta of \(\beta_f\)) required for a cash equitization operation can be determined as follows:

$$
N_f= \left[\frac {\beta_T}{\beta_f} \right]\left(\frac {S}{F} \right) $$

Question

Kohei Yamamomo is an equity portfolio manager at a bank in Osaka, Japan. He is optimistic about the Brazilian equity market (“BOVESPA”). Due to his optimism, he used an equity swap to adjust his exposure away from the Japanese equity market (“NIKKEI”) and toward Brazilian equities. Yamamomo would most likely enter.

1. Pay BOVESPA; receive NIKKEI.
2. Receive fixed rate; Pay BOVESPA.
3. Receive BOVESPA; Pay fixed rate.

Solution

The correct answer is C.

The manager wants to increase exposure to the BOVESPA, so receiving its return makes more sense than paying it. This eliminates options involving paying the BOVESPA return. The choice between a fixed rate and the return of the NIKKEI becomes secondary, but it's not given as an answer choice.

A and B are incorrect. They go against Kohei Yamamomo's objective of increasing his exposure to the Brazilian equity market (BOVESPA) due to his optimism about its performance.

Derivatives and Risk Management: Learning Module 2: Swaps, Forwards, and Futures Strategies; Los 2(c) Demonstrate how equity swaps, forwards, and futures can be used to modify a portfolio’s risk and return