# The Missing Link

Most well-read investors are aware of the need to hold both
bonds and equities in their portfolio. Even though these instruments often have
correlated returns, the diversification benefit and the periodic boost through
active rebalancing still mean a stock/bond portfolio is better than stocks
alone. “Better” can be measured in many ways but we can keep it simple.

Since June of 2004 (a starting period that will make sense
later):

·
A 60/40 mix of equity and bonds had an average
annualized return of 10.6% and annualized volatility of 11.0%. Maximum drawdown
was 36.8%.

·
The S&P 500 (including dividends) had an
average annualized return of 7.6% and annualized volatility of 19.4%. Maximum
drawdown was 56.8%.

This is a decisive victory for the idea of a portfolio over
just equities. This idea can be extended to other asset classes as well. For
example, we could include commodities and real estate.

But in the last few decades several products have been
developed that depend in some way on volatility. These have given rise to the
concept of volatility as an asset class. Here we will show that a volatility
position can improve both the return and Sharpe ratio of a portfolio when
compared to one with the traditional mix of stocks and bonds.

The basic idea of volatility is familiar to any investor.
Volatility is a measure of the variability of an asset’s returns. It is often
used as a measure of risk. Any time we have historical return (or price) data
we can estimate what volatility has been. Volatility is defined as the standard
deviation of the returns, and the larger this number, the larger the moves of
the underlying asset. Volatility varies in time due to the influence of
macroeconomic events such as inflation, unemployment and money supply; microstructure
effects such as intrinsic crashes and squeezes; and external events such as
terrorist attacks, earthquakes and elections. This variability of volatility
means there are many nuances in measuring past volatility and even more in
forecasting future volatility.

There are two main types of volatility. Realized volatility
is the variability of the underlying. Implied volatility is the volatility
predicted by an option pricing model. Realized volatility can be traded through
variance swaps and volatility swaps but these are not available to most
investors. An easier way to trade volatility is through implied volatility.

Implied volatility is option pricing model dependent, but it
is possible to use all the option prices for one expiration on a given
underlying and recover a model free implied volatility. This is the idea behind
the calculation of the VIX index, a model free, 30 day, implied volatility
index for the S&P 500.

Implied volatility, whether from options themselves or from
the VIX futures, tends to be overpriced relative to subsequent realized
volatility. We can see this by comparing the level of the VIX to the subsequent
30 day realized volatility. The average premium since 1990 has been 4.2
volatility points or 23% of the VIX level.

(VIX is in blue).

The easiest way to see why implied volatility would be
overpriced is to realize that people buy options as insurance against something
that might happen. Puts give protection against price drops and calls protect
from the regret of missing a rally. And just as with life and property
insurance, people are prepared to pay a premium for this protection. Insurance
buyers aren’t being stupid. Their evaluation of their personal exposure to risk
makes the purchase sensible, even if it is expected to lose money.

Because implied volatility is usually over-priced we can
make money selling it. Unfortunately, it isn’t directly tradeable. There are
several ways to get short implied volatility exposure and each has some
wrinkles associated with it. One way would be to sell options then dynamically
hedge them. While this is a legitimate idea, it is not a pure implied
volatility play: there is also exposure to the realized volatility.

We can also choose to sell VIX futures. VIX futures are
unusual. Standard economic thinking tells us that a future price should be an
unbiased predictor of the underlying price when the contract expires. This is
untrue for VIX futures. Instead the futures tend to move towards the VIX index.
So, if VIX futures are higher than the index, we can sell them and expect that
they will fall. And as the VIX futures usually are higher than the index, we
will expect to make money being short VIX futures.

The CBOE publishes a strategy index, VPD, which combines a
money market account with short front month VIX futures (details can be found at
http://www.cboe.com/micro/vpd/default.aspx).
The exact number of futures corresponding to a given notional investment will
vary slightly depending on money market rates but currently one future would be
held for each $100,000.

Below we show the performance of VPD since June of 2004 (I
said this date would be relevant). Average annualized return has been 18.8% and
annualized volatility has been 20.8%.

Even though volatility and equity have negative correlation,
the exceptional returns of short volatility mean that the best way to help our
portfolio is to replace some long equity with a short volatility position.

Moving just 2.5% of the portfolio from equity to a short
position in front month VIX futures led to an average annualized return of
12.3% and annualized volatility of 10.9%. Maximum drawdown was 38.1%. Adding
short exposure to the portfolio increases returns and lowers risk, whether we
define this in terms of volatility or drawdown.

But we can do much better. As we hinted at when we discussed
the general properties of volatility, it is much more predictable than equity
prices. Talton uses several models to time the volatility markets and trades a
dynamically adjusted option portfolio. This can’t be directly compared to the
VPD allocation because the margining is different, so let’s take a concrete
example. In 2016, the basic 60/40 portfolio would have returned 8.7% with a
volatility of 7.5% and a drawdown of 5.6%. Changing this allocation to 50%
equity, 40% bonds and 10% at Talton changes these results to a return of 10.3%
with a volatility of 6.6% and a drawdown of 4%.

There are many ways to get a short volatility exposure. You
can use strategies involving futures, options and an almost infinite number of
combinations of these derivatives. And depending on exactly how you choose to
invest in volatility, the amount of your portfolio to commit will be different.
But however you choose to get this exposure, you really need short volatility
in any portfolio. It is the missing link.