Why two modest strategies can share a higher Sharpe

LessonThis is a lesson restated in new words. Any figure in it is an example from the source, not this desk's record.

A single backtest with a Sharpe ratio of 0.8, a max drawdown around 15 percent, and a total return around 13 percent can be a real description of a path and still be a weak book. The lecture's move is not to keep tuning that one rule until the ratio looks better. It is to add a second strategy whose results do not move with the first. In the example, the second has a Sharpe ratio of 0.9. An equal mix of the two prints 1.2.

Why it matters

The point of the book, in this talk, is to make money and to stay solvent. A higher ratio from diversification is attractive because it is a smoother path for a given pair of results, which is what would let you use leverage without the drawdown that ends the account. That sentence depends on the smooth path surviving the moment when everything falls together. If the two strategies only looked independent in the sample, the 1.2 is a description of the past mix, not a property you can lever.

The opening numbers are modest on purpose. The lecture says the 0.8 might even be free of look-ahead bias and might have some forward content. It also says the ratio is not impressive, the payoff is not one-to-one, and you have not yet asked whether a regression on the S&P 500 would swallow the result. Alpha is postponed. Structure comes first.

The idea in plain words

Two equity curves that do not resemble each other are the hint. Weight them half and half. The lecture shows the combination stepping from 0.8 and 0.9 to 1.2. The mechanism is the usual one: when one is in its drawdown, the other is not required to be, so the mix varies less than either piece. Less variation with both pieces still contributing return is a higher Sharpe ratio. You did not find a better entry. You changed the portfolio.

The failure mode is hidden in "do not resemble." If both books are US equities, they are not physically independent, and the lecture says they are therefore not stochastically independent either. In a market break, the correlation structure that produced the pretty mix comes apart. Correlations move toward one. Both strategies fall together. The mix's path stops being the smooth one you sized off.

The contrast is a book that is half US equities and half something the lecture says has nothing to do with that selloff. The example is making markets in sports contracts. An equity crash does not, on this claim, decide those contracts. The top chart in the talk is that kind of mix, and the equity curve stays smoother through the drawdown. The bottom chart is two US equity strategies, and the same drawdown shows up in the mix. Physical independence is the phrase they want. Arbitrary diversification, two tickers in the same storm, is not it. Physical independence, they add, implies stochastic independence. The goal they state at the end is a smooth curve and a reasonable ratio of return to risk, so that leverage is not a bet on surviving one correlation spike.

How to use it

Do not grind one rule only to inflate its ratio. Put the two in a book, as in the step from 0.8 and 0.9 to 1.2, then ask what both hold when equities fall. If the answer is the same beta, the independence was fair-weather.

A sports-contract sleeve is the lecture's concrete picture of a different exposure, not a recommendation with a history attached. No return for that sleeve is stated. The chart claim is qualitative: the independent mix draws down less than the two-equity mix when equities break.

What usually goes wrong

The 1.2 gets levered because the sample curves were uncorrelated. The bottom chart is the selloff where that correlation fails. Tuning one rule until it looks like the mix is the wrong job. Two US equity books are still one storm.

Questions people ask

What ratios did the lecture actually combine?

A strategy at a Sharpe ratio of 0.8, with max drawdown around 15 percent and total return around 13 percent, and a second at 0.9. Half and half, the mix was 1.2.

Why would that mix fall apart?

If both sides are US equities, the lecture says they are not independent, and in a break their correlation moves toward one. The smooth equity curve was a fair-weather fact.

What counts as independent here?

A sleeve whose payoff the lecture says an equity crash does not decide. The example is sports contracts. No performance number for that sleeve is given. The claim is about the drawdown of the mix, not a promised return.