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The Long and Short on Long-Short 347
interest rate risk if the performance is linked to a floating rate, but it
may reduce risk for an equitked long-short portfolio (for instance, if
the maturity of the investment matches that of the stock index
futures contracts used as an overlay on the portfolio).
8. The return spread of 6 percent is achieved in this example with a
long return exceeding the market return by 3 percentage points and
a short return falling shy of the market retum by 3 percentage
points. The market return is provided solely for illustration and is
irrelevant to the return spread (as will become evident later, in the
discussion of "integrated optimization"). Any pair of long and short
returns where the longs outperform the shorts by 6 percent provides
the same return spread, regardless of the market's return.
9. Such an argument is made by Michaud (1993), who assumes that
(using his notation):
and
a, = a,
W, = 0,
or the excess return and residual risk of the long positions in longshort
equal the excess return and residual risk of the short positions.
He also implicitly assumes that the excess returns and residual risks
of the long and short positions equal the excess return and residual
risk of an index-constrained long-only portfolio. That is:
and
a~ = C% = cllong+dy
"L = "S = qong-ody
From these assumptions he concludes that
where r equals the ratiof portfolio excess return to portfolio
residual risk. Thus, the long-short portfolio can offer no benefits ove
a long-only portfolio except to the extent that the correlation
between the excess returns on its long and short positions, p, is less
than 1. But such diversification benefi,ts can be obtained by
combining any assets that are less than fully correlated.
10. A consideration in equitizing a portfolio is the use of a tail hedge.
See Kawaller and Koch (1988).