Thread by @breakingthemark

Showing why vol targeting produces a higher compound growth rate portfolio, through coin flips.

Odd rounds, heads: +10%, tails -10%

Even rounds, heads: +20%, tails -20%

Both games average 0% gain each flip. The even rounds have 2X the volatility of the odd rounds though.

This game is supposed to mimic how markets have variable stable volatility. There are periods of high vol and period so of low vol.

Total volatility for this game is sqrt(10%*10% + 20%*20%)/2 = 15.8%

Vol drag is 15.8%^2 /2 = 1.25%

Now let's vol target the game. On odd rounds bet 140% the base bet, and on even rounds bet 70% of the base bet. The outcome of each flip becomes:

Odd rounds, heads: +14%, tails -14%
Even rounds, heads: +14%, tails -14%

Each round is now identical, with same vol and return.

Realized vol for the strategy goes down.

Volatility for the vol targeted game is now 14%

Vol drag is now 14%^2/2 = 0.98%

By targeting a stable volatility, the realized volatility went down, while the arithmetic return stay the same (0%).

Therefore, the compound growth rate is higher with the vol-targeted strategy than the base strategy.
CAGR = Arithmetic Return - Vol Drag.

Sharpe ratio is also higher for the vol targeted strategy.
Sharpe = Arithmetic/Volatility

Vol targeting benefits the overall portfolio.

This works because volatility is combined through variance (vol squared), and vol drag comes from variance.

Because vol is squared, trading increasing lower vol regime volatility with lowering higher vol regime volatility leads to lower combined portfolio variance.

The most “efficient” form of volatility is stable, consistent volatility.

Therefore, even though you can’t perfectly balance volatility in the real world, moving towards smoother volatility will can potentially increase portfolio CAGR and Sharpe.