Dec

19

How does the arithmetic average differ from the geometric average in measuring returns?

The arithmetic average calculates the average gain per trade without accounting for the compounding effect. On the other hand, the geometric average (CAGR) considers the actual compounding from start to finish, providing a more accurate measure of the actual return.

Can positive arithmetic averages lead to losses or ruin in trading?

Yes, even with a positive expected arithmetic average, losses or ruin are possible due to the risk of ruin and the increased burden in recovering from drawdowns, . Geometric averages, considering drawdowns and compounding, offer a more realistic view of potential outcomes.

From quantified strategies.

This is the path dependency issue. Conclusion is position sizing is important to avoid risk of ruin or catastrophic drawdown.

Bill Rafter responds:

You are almost there. Think: can these two means be used to identify anything else?

Kora Reddy adds:

also called volatility drag:
vol_drag = mean(x) - exp(mean(log(x)))
or an approximated formula
Volatility Drag = -0.5* (Volatility)^2
PFA useful leteratrue

Zubin Al Genubi replies:

The expectation and the maximum drawdown can be used to compute optimum f, the fixed fraction of capital to risk on each trade.

I read the article [on volatility drag] and disagree with it. Ralph Vince says that a system will experience drawdowns equal to f and that is the only way to the highest compounding resulting return. It is impossible to get the return without the volatility. Diversifying systems can counter balance drawdowns if truly uncorrelated.

It is non-ergodicity of trading markets that make the geometric mean more important. A loss is not a straight line down, but convex because it takes a 100% gain to recoup a 50% loss. The geometric mean captures this. Arithmetic mean does not.

Big Al offers:

Shannon's Demon, or rebalancing between uncorrelated assets (they claim it's "little known", but that is doubtful).

Kim Zussman contextualizes:

"Say, your fund is down almost every year. What value do you add?"

"We're uncorrelated! (with buy and hold)."


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