It has been a strange month in the markets. Not only is the S&P 500 off to it’s fastest collapse from an all time high ever, other assets are collapsing as well. Stocks, bonds, and gold sold off the most they ever have in unison on March 11th, only to fall more on March 18th.
Lets take a look under the hood and try and understand why this is happening from my heretical view of market behavior.
What is Going On Right Now?
Simply, the market is reacting to increased uncertainty. The coronavirus has made the future very unclear.
- Will the market rebound like a rocket? Will it bounce back up (and beyond) the old highs in short order?
- Will the market linger around these levels for a while?
- Are we at the start of another great depression?
All of these views are perfectly valid.
Uncertainty is very high.
Uncertainty and volatility are essentially the same thing. When they are rising, the market should react in a certain way.
Maximizing Geometric Return
I believe that markets work to maximize their own geometric return. This means they strive to price assets at the proper ratio to achieve this goal.
The Math behind maximizing the geometric return is fairly straightforward for a few assets. I discussed simple versions in two previous posts here and here.
Conceptually, I have presented this idea through mixing ranges. The mixing ranges consist of the asset’s arithmetic return minus it’s variance (standard deviation squared).
The proper weight of each asset in the portfolio is determined by comparing these mixing ranges.
So for this example, the allocations to maximize geometric return is
- 46% of the portfolio in asset #1
- 54% of the portfolio in asset #2
(asset #1 is 6/13=.46, for example see this).
Crisis Increases the Standard Deviation
The above example uses a standard deviations of 20% for asset #1 and 30% for asset #2 (and a correlation of zero). What happens if we push both standard deviations up? Let’s say to 30% and 40% respectively.
Now the proper portfolio becomes:
- 52% in Asset #1
- 48% in Asset #2
When standard deviation (uncertainty) increases, you should reduce exposure to the asset with the largest volatility. The wealth then flows to the asset with the least volatility.1
I’ve outlined before how, since there is a buyer and a seller for every transaction, the only way for the “market” to move wealth from one asset to the other is for the price to rise in one, and fall in the the other.
With uncertainty exploding and stocks selling off hard, that’s exactly what has been happening.
Some of the time.
Where Cash Changes Things.
Cash can get in the way of this balance . The math is very complicated as wealth flows between multiple assets. But thankfully its straight forward with one asset, or one portfolio. So we will start there.
Let’s imagine a diversified portfolio of stocks, bonds, commodities, real estate, etc, which has a 6% arithmetic return and a typical standard deviation of 10% (annualized values), with the risk free rate at 1.5%.
The bottom of the “mixing range” for the S&P 500 is rarely near the risk free asset. The same is true for bonds, and a diversified portfolio. Since the risk free rate is not inside the mixing range, the geometrically optimal portfolio does not include any cash.
So what happens when the portfolio’s standard deviation increases?
At first, an increase in standard deviation from 10% to 20% doesn’t lead to any movement toward cash (assume no leverage). The maximum geometric return is still realized by holding the portfolio in full.
Now as the volatility of the portfolio increases, the internal component allocations should change. The ratio of bonds to stocks to commodities will adjust and evolve similar to the way the allocations of the two assets adjusted above. However cash still rests outside the mixing range and therefore will be left “untouched”. The total wealth inside the preferred portfolio isn’t falling, its just shifting from asset to asset.
However when the portfolio volatility rises to 22.3% a shift occurs.2 As shown below with the volatility at 25%, the risk free rate (cash) is now inside the mixing range. And the rational, return maximizing, action is to sell off part of the portfolio to increase the cash holdings.
From the market’s perspective, this move to “sell off part of the portfolio” occurs though falling asset prices.
This Is Why Correlations Go To “1”
I believe this is why correlations go to “1” in times of crisis. When the market “sells off part of the portfolio”, it’s “selling” everything.
The risk free rate’s position relative to the market portfolio’s return determines when correlations to go to 1, creating a simultaneous fall in asset prices. Once the portfolio variance crosses this threshold, assets will start falling in sync with each other.
Often the internal dynamics of the portfolio composition shift (asset to asset) flowing strongly into treasury bonds. In past crashes, I believe this “asset to asset” flow counteracted the overall portfolio’s push into cash, propping bonds up. But the last few weeks even bonds felt the selling pressure.3
Seeing the Move in Action
A week and a half ago, I noticed assets were becoming more correlated and stated that could be a problem.
I feared the rising correlations signaled the “market” had already started moving into cash.
The next day the S&P 500 fell 10% . It fell 16% through last Friday. Gold fell 4% the following day and 9% in total. Bonds barely rallied the next day, and then proceeded to fall 8% over the following 4 days. Everything lost money. There was a flight to cash.
Most people say this was due to margin calls. There probably were margin calls. Others said Risk Parity funds were blowing up. I’m sure some were deleveraging during this time, but I haven’t seen any evidence they blew up. I believe the market was just chasing the correct portfolio allocations to maximize its geometric return.
Is The Flight To Cash Over?
No idea. Volatility is still high in the markets. Uncertainty about the future of the virus still seems high to me too. The risk free rate can’t really be lowered any further as a way to ease the pressure from cash. I would assume any major spike in volatility from this point forward will produce a similar reaction downward in all assets.
If its not clear, the relationships here are very complicated. This example simplifies the true dynamics of the market. But hopefully I’ve provided a framework for understanding the big picture relationships.
Next time volatility spikes in the market and correlation starts evolving, I hope you will think about this framework. I find it very useful to explain what is happening in the market and what risks lie around the corner. I’ve built my investing strategy around these ideas. So far it’s worked well. Maybe incorporating these ideas into your investment strategies will also improve your results and increase your wealth.
1-By higher returning I mean the higher arithmetically returning asset, not the higher geometrically returning asset.
2- 0.05 ^0.5 = 0.223
3-Its likely bonds fell because their standard deviation exploded upward more so than in prior crashes.