## What is Volatility and Why it Matters?

Volatility is a measurement of risk in the stock market, high volatility would translate to a higher probability of the extreme events of striking it rich or going broke. Is this really true? In the next article, we will explore the mechanics which drive volatility lower and find how volatility is used not just as a measurement of risk but as an input for risk-taking.

Either way, what remains true is that volatility could provide investors with a hedge against their equities’ downside risk, specifically their left-tail risk. Volatility spike is more common when the stock market is crashing.

It is important to understand that VIX is forward looking. VIX reacts to the sentiments of investors through S&P 500 options’ premium prices. If premium increases, it would mean that investors are expecting the market to be more volatile. Read on the VIX White Paper to learn more.

## Is it Worth to Long Volatility?

The caveat with volatility is that a premium had to be paid periodically. In some cases, even if the market did crash, you had paid so much in premiums that you are still net negative on your volatility component. E.g. You have paid $100 in premiums for the past 5 years but only got$90 back when the market crashed. But, it is crucial to remember that if instead of insurance, you went with placing more of your portfolio into equities, during the crash, these added equities would also be making a loss. Instead of just seeing how much the volatility made in terms of its return, it would make better sense to view how much it prevented you from losing.

It is crucial that we use the right metrics when measuring various financial tools. In this case, we use volatility as a hedge against equity losses from a market crash. So, there is little meaning behind using returns to measure how well performed. Making returns was never its job in the first place! Instead, let’s measure how much it protected your entire portfolio had you no volatility component.

So, now let’s imagine three scenario where total premiums paid up to a crash is $20k and the market crashed by 50%: 1. No volatility hedge 2. Volatility hedge that covers all equity losses during crash 3. Volatility hedge that partially covers all equity losses during crash 4. Time decay on premiums cost so much that even after crash, money was still not made back after market crash Scenario 1: lost$50k.

Scenario 2: lost $0 but effectively lost$20k due to paid premiums ($100k –$80k).

Scenario 3: lost $40k ($20k from premiums and $20k from the crash). One important thing to note is that in this scenario, the volatility hedge had in reality not made any profits! It cost$20k in premium and made $20k back during the crash. Meant that it had in fact only made back what it cost, yet was still able to save us$10k had us not hedged.

Scenario 4: Even after the crash, the return on the volatility component is still net negative. In this example, $10k was made back from the crash.$10k was lost in total (earnings – premiums = $10k –$20k = -$10). Even then, it would be equivalent to scenario 1 where post-crash leaves the portfolio at$50k. Even in this scenario, it is lose an equivalent amount to not hedging.

I hope that scenario 4 has shown how using the right metric to measure volatility is crucial. Do not remove all components of your portfolio that does not make positive returns. Analysis and understand what other benefits they bring to the table, do not be over-fixated on one metric.

### Overview of Portfolio Theory – Not All Returns are equal

In the above graph, Asset C (volatility) provides you with zero returns but the upside is that it is negatively correlated to Asset A and B (equities) which has positive returns but undergoes extreme ups and downs (bulls and bears). Most people might think to load up on A and B so as to ride the wave up, even if there is a market crash and suffers a large dip, it is still positive returns over a long enough time horizon.

But instead, having a mix of zero return negatively correlated C and the high returns volatile A gave the best results. The reason is compounding.

Not all returns are equal.

There is not much difference between a -1% or +1% return. What about +50% and -50%?

Between +50% and -50% which is more significant? It might make intuitive sense that that they are equivalent. They are both 50% after all, right? Against intuition, the 50% decrease is more significant. You would need to get a 100% return to get back to your original amount! While for the 50% increase, you only need a -33% to get back your gain.

$\dpi{150}&space;\\\text{Where&space;x&space;is&space;the&space;inital&space;%&space;decrease&space;in&space;portfolio;}&space;\\\text{y&space;is&space;the&space;years&space;taken&space;to&space;return&space;to&space;original&space;amount}&space;\\\\(1-x)\cdot(1+\text{%&space;gain})^{y}=1&space;\rightarrow&space;\text{original&space;amount}&space;\\y=log_{{(1+\text{%&space;gain})}}\frac{1}{1-x}$

Due to how the decrease x in portfolio is in the numerator, every 1% decrease in portfolio value x increases y significantly more as shown here.

I have also created a simple form below that you can play around with to see the effects of negative returns.

Even with a small market crash of 30%, without insurance on your portfolio would mean 5 years to revert back to its original value. And that is just the nominal interest, not taking into account inflation. If we used the 50% S&P 500 market crash in the 2008, it would equate to 0% return for 10 years!

That is why hedging is crucial to your portfolio. Even psychologically, it would help since you would never see your portfolio in the deep red, you would not be swayed by thoughts of ‘selling it early to cut losses’. It can keep you rational in the most irrational of times. Volatility is just one of the ways you can hedge away your portfolio’s downside risk.

## Conclusion

Yes, long volatility is worth it, as it reduces equity risk. The better question is how much should should the long volatility weightage be?

### What about Bonds?

But, what about bonds? Don’t bonds have a negative correlation to equities? And it also have a positive carry which is the main disadvantage to long volatility.

The 60/40 (equity/bonds) performed amazingly well for the past 40 years. From 1984-2007, the annual return averaged 13.7%. From 2008-2019, the annual return average 9.4%.

Past performance is not indicative of future results. What is important is understanding the mechanics behind the performance of 60/40 portfolio. With yield at zero-bound, unless interest goes into the negative, there is little upside with holding bonds.

It is likely that bonds have ran out of ammunition to continue being the source of diversification against equity.