Matched straddles on levered versus unlevered index proxies

A dollar-matched comparison after the shock

A few sessions after an early-May index shock, an options straddle, a same-strike, same-expiry long call and put, was used to compare two index vehicles on similar dollar risk over weeks to months. The index-proxy pair was a two-times daily S&P 500 fund and an unlevered S&P 500 fund, each started from the at-the-money strike, the front-month strike nearest the close, so both packages began from comparable moneyness.

The two-times S&P 500 proxy closed at 40.86 against a May 41 strike. The unlevered S&P 500 fund closed at 115.83 against a May 116 strike.

Matched-dollar-risk sized each straddle so outlay was a similar share of a small book rather than matching share count or notional. On a hypothetical 50000 book risking just over 2 percent per line, four May 41 straddles on the leveraged proxy at 2.75, an 1100 outlay, were treated as a near-dollar match for three May 116 straddles on the unlevered fund at 3.87, a 1161 outlay. Under that construction the three unlevered straddles cost about 6 percent, or 60 dollars, more than the four leveraged straddles.

Implied volatility and the breakeven band

Implied volatility is the volatility already quoted in each straddle. Quoted implied volatility was 50.5 on the leveraged-proxy straddle versus 25.3 on the unlevered-fund straddle, a near doubling in line with the two-times daily design.

The breakeven-band is the underlying percentage move each straddle needs before expiry to recover the premium paid. Leveraged-proxy breakevens of 43.75 and 38.25 implied about a 7 percent upside move and a 6.50 percent downside move from 40.86. Unlevered-fund breakevens of 119.87 and 112.13 implied about a 3.50 percent move higher and a 3.20 percent move lower.

Greek scaling on similar cash outlay

Greek-scaling asks how delta, gamma, theta, and vega of a leveraged-proxy package compare with a dollar-matched unlevered package. Both packages were near delta-flat. Gamma on the leveraged package was 93 versus 49 on the unlevered package. Theta was similar at -54 versus -58. Vega was 22 versus 46.

After implied volatility and the Greeks were scaled to the leverage and similar cash outlay, the side-by-side left little residual gap between the leveraged proxy and the unlevered index fund.