Volatility matters

probability of tiger attack-definition of market-tax you pay unknowingly-falling down the logarithmic curve- Sharpe can make you poor-never lose the principal

If I am a resident of a forest famous for man eating tiger, only thing that matters is that knowledge-there are tiger out there; not the probability of tiger attacking me nor their number. That holds true even when I am on a half day visit to the forest, not necessary having applied for a residency there.

Once again, what really matters is “are there any tiger out there?”, not “when she will come?”, “how many tigers are out there?” nor “how often they attack men?” Market can be likened to a forest. Just as you might encounter a man-eating tiger in the forest, draw-downs in the market can be equally dangerous for your portfolio. But you also often get pleasantly surprised with delicious fruits—great returns. Above all, the market, like the forest, is unpredictable.

Long back, one of my collogues asked me to explain market and predict what will happen when. I told him,

“Market is what market does: It fluctuates”

Market fluctuates; it fluctuates violently in either directions; it fluctuates violently in either directions stochastically; it fluctuates violently in either directions stochastically with periods of stochastic quiescence in between. We can never know when it will fluctuate, how many times it will fluctuate, in what direction and sequence it will fluctuate.

We always welcome upward movement. We want market to move upward more frequently and more violently. Problem is that market can also move down and it often does. Below is the 5 year annual return of Nifty 50 index:

Year	Return
2007	+54%
2008	-52%
2009	+76%
2010	+18%
2011	-25%

We can evaluate the returns for this period either using arithmetic mean or CAGR. Arithmetic average return during the period is 14.2% (annual), but the CAGR is just 2.86%. Arithmetic average does not really matter, what really matters is the CAGR. It determines your final TPV (total Portfolio Value), if you have lump-sum investment at the starting period. It is what you have realised.

If we can magically remove the 2 big draw-downs to zero, the CAGR becomes 26.2%!!. 23.32 is the volatility tax you paid unknowing during the period. Volatility tax eats from your principal.

If you lose 1% of the principal, to get back to 100%, you need 1% return. If it is 5% lose, you need little more than 5% to recover. This increases exponentially when the lose increases, by the formula:

\[ (x/(100-x))100 \]

It is just like walking towards the crest of the water fall. Instead of waterfall, here you fall down from the crest of logarithmic curve.

Loss	Return need to reset
1%	1%
5%	5.3
10%	11.1%
20%	25%
40%	66.67%
50%	100%
75%	300%
95%	1900%
100%	∞

Modern portfolio theory attempts to address the problem of volatility through diversification and proposes the Sharpe ratio to evaluate the risk-adjusted return of a portfolio. It reduces downward volatility to some extent, but in doing so, it also reduces favorable upward movements, prescribing a cure that may be costlier than the disease—ultimately leaving you in a zoo instead of a grand forest, out of fear.

This takes us back to the fundamental law of investment: Never lose the principal. Try to achieve this without reducing the overall return, as you might otherwise end up poorer.