Alternative treatments of equitized hedge funds

By William K.S. Wang

Increasingly, institutional investor portfolios contain equitized hedge funds, which are hedge funds combined with stock index futures.

This article examines how to treat such vehicles when comparing the actual portfolio with the organization's target or benchmark portfolio and any portfolio restrictions.

Suppose an institutional investor holds $1 in hedge funds plus $1 in bonds and has no other assets or liabilities. The net worth is $2.

The investor can equitize the $1 in hedge funds by purchasing $1 in stock index futures. The stock index future is a contract to purchase $1 of the stock index in the future.

By equitizing the hedge funds, the investor combines the return on the overall stock market (or beta) with the return on the hedge funds. If, as anticipated, the return on the hedge funds is positive, the investor obtains a package that outperforms the overall stock market.

(Hedge funds might have a small positive correlation with the overall stock market. For simplicity, I shall assume the investor does not buy less than $1 of stock market index futures to try to achieve a beta of 1 on the hedge fund/future package, i.e. a correlation of 1 with the overall stock market. For simplicity, I shall also assume the institution can enter into the futures contract without posting any performance bond.)

One question is how to treat the $1 stock index future on the list of portfolio assets, liabilities and net worth for the purpose of comparing the actual portfolio with the organization's target or benchmark portfolio and any portfolio restrictions. If the investor treats the $1 stock index future as an asset with no further adjustment, the portfolio's net worth will falsely appear to increase by $1:

Assets: $1 in hedge funds, $1 in stock index futures, $1 in bonds.

Liabilities: None.

Net worth: $3.

Many institutional investors treat $1 in hedge funds and $1 in stock index futures as equivalent to holding $1 in an actively managed stock portfolio (sometimes called portable alpha). Just as hydrogen and oxygen chemically combine to produce water, the $1 in hedge funds and $1 in stock index futures combine to produce $1 in an actively managed stock portfolio:

Assets: $1 in an actively managed stock portfolio (receiving returns on both $1 in hedge funds and $1 in the overall stock market); $1 in bonds.

Liabilities: None.

Net worth: $2.

The problem with this approach is its suboptimal treatment of the imputed or embedded debt in the index future.

I argue for either of two alternative treatments:

• $1 in hedge funds, $1 in a stock index fund, $1 in bonds, plus a liability of $1 in short-term borrowing; or

• $1 in hedge funds and $1 in a stock index fund.

First alternative

Assets: $1 in hedge funds, $1 in a stock index fund, $1 in bonds.

Liabilities: $1 in short-term borrowing.

Net worth: $2.

The $1 stock index future is equivalent to borrowing $1 short-term to purchase $1 of a stock index fund. The reason is that the price of the index future is determined by sellers of the instrument who borrow short-term to buy the index for future delivery. One could view the instrument-seller as the agent of the instrument-buyer. On behalf of the buyer, the "agent" borrows to purchase the stock index fund. At "settlement," the "agent" sells the "buyer's" index fund shares and repays the "buyer's" loan plus interest. If the balance is positive, the "agent" sends that amount to the buyer. If the balance is negative, the "agent" collects that amount from the buyer.

Second alternative

The second alternative treatment assumes the first alternative treatment is valid and varies it further. Suppose the institution's $1 in bondholdings are in short-term instruments. The $1 in short-term bonds would roughly offset the $1 in short-term borrowing. The organization could cancel both the short-term borrowing and the short-term bondholdings. The result would be:

Assets: $1 in hedge funds, $1 in a stock index fund.

Liabilities: None.

Net worth: $2.

The offset of the bondholdings and the liabilities would be not for the purpose of the balance sheet but for comparing the actual portfolio with the institution's target or benchmark portfolio and any portfolio restrictions.

Suppose the $1 in bondholdings were in longer-term instruments. The $1 in short-term borrowing would be a less exact offset to the $1 in bondholdings. Nevertheless, the organization might still offset the two to obtain the rough equivalent of $1 in hedge funds and $1 in a stock index fund.

Only a small difference exists between the following portfolios:

(1) $1 in hedge funds plus $1 in a stock index fund.

(2) $1 in hedge funds, $1 in stock index futures, plus $1 in bonds, which in turn is equivalent to $1 in hedge funds, $1 in a stock index fund, $1 in bonds, plus $1 in short-term borrowing.

With the second portfolio, the investor both borrows $1 and lends $1 and, relative to the first portfolio, gains only any difference between the cost of borrowing and the return from lending.

This article started with an assumption that the organization holds $1 in hedge funds plus $1 in bondholdings and has no other assets or liabilities. Actually selling the $1 of bonds to buy $1 of a stock index fund is not that different from equitizing the $1 of hedge funds.

In summary, an institution that purchases a $1 stock index future is in effect borrowing $1 to invest in a stock index fund. This $1 liability may roughly offset $1 of bondholdings.

William K.S. Wang is a professor at the University of California, Hastings College of the Law.