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The Effect of Crazy Time on Portfolio Allocations
I am continually fascinated by how many second-order ‘understandings’ are missed, even by those people who have a really good first-order understanding of finance. For example, every financial advisor understands that bonds are less volatile than stocks. Most financial advisors understand that stocks and bonds in a portfolio together also benefit because they’re not correlated. Some financial advisors, and most CTAs, understand that diversifying a portfolio works because when you add uncorrelated assets together, the risk of the whole is less than the sum of the risks because of the offset from the correlation effects. Those are all coarse understandings that any financial professional should ‘get.’ However, it is fairly unusual for advisors or even CTAs to understand that the correlation of stocks and bonds undergoes a state shift when inflation get above about 2.5% for a few years, and become correlated, and that means more risk for the same combination of stocks and bonds. Here’s that chart I love to show, updated through the end of the year.
While that’s an example of a ‘second-order understanding’ that isn’t widely known, it isn’t what I want to write about today. Actually, for a change what I want to discuss is something that has nothing directly to do with inflation, and that is the effect of volatility on asset allocation.
This is an important discussion right now, because whether or not you have gotten the message yet that President Trump is going to be much more Machiavellian in his approach to the global world order than prior Presidents have been – and whether you think that’s a good thing or a bad thing – you surely must have noticed that the volatility of the markets under this regime is likely to be somewhat higher than under Sleepy Joe and also higher than it was during Trump’s first term. And that leads to the second-order understanding about what that implies for markets. Hang with me here; if you’re not a finance person this gets a little hairy.
The next chart shows Modern Portfolio Theory on one chart.
The blue line is the Markowitz efficient frontier: every point on the line represents a portfolio of assets that is the least-risky for that level of expected return. So, the highest vertical point is a portfolio of 100% in the asset with the highest expected return…you can’t get more return without leverage.[1] In this case, let’s assume that is equities. As you go down the curve, you allocate more to other less-risky assets and give up some portfolio return. Because assets are not 100% correlated, you can always get a portfolio that has at least as good (and usually better) returns for a unit of risk than any single asset – that’s the benefit of diversification. As you get to very low expected returns, you get to the part of the curve you’d have to be irrational to be on because you get higher risk and lower returns, and so we usually ignore that part of the curve that bends back.
The red line is popularly called the “Capital Asset Line.” Assuming there is some zero-risk instrument (that’s not already in the assets we’ve considered, so there’s some hand-waving here) and you can both borrow and invest at that rate, you can think of a portfolio that is the ‘best’ portfolio on the blue curve, either combined with the zero risk instrument (sliding down the red line to the left) or levered at the zero risk instrument (moving up the red line to the right). The ‘best’ portfolio here is defined as the place where the red curve is tangent to the blue curve.
A lot of times you’ll just see those two lines, but it doesn’t answer the question of which portfolio an actual investor prefers. It turns out that investors do not have linear risk preferences…that is, if I make my portfolio 10% more risky, perhaps I require 1% more return but if I make it another 10% risky, I’m going to need more than 1% additional return. I’m not only risk averse, but I get more risk averse the larger the potential risks. [Lots of experimental data on this. If I offer you a bet where you pay me $1 and on the basis of a coin flip I will either pay you $2 or $0, you are much more likely to take that bet than if I offer you a bet where you are risking $10,000 for the chance at $20,000…or zero]. So the purple dotted line is a hypothetical ‘investor indifference curve’. I just made up that term because I can’t remember what the theoreticians call it. The curve represents all of the combinations of risk and return that make the investor equally happy. So, the best portfolio for this investor is where the purple line – the highest purple line we can find, indicating the MOST happiness – touches the red line.
With me? Now consider the next chart. All I have done here is to increase the risk of every asset and shift the whole portfolio efficient frontier to the right.
What happens? The Capital Asset Line (red) now flattens out. And that means that the prior purple line no longer has a point of tangency. We have to go to a lower purple line, and since the purple line is concave upward the red line becomes tangent to the purple line at a point further to the left (the slope of the red line is flatter, and the flatter parts of the purple line are to the left). I’ve put the new ‘optimal portfolio’ as a dot in purple.
The implication is this: if overall risk in markets is perceived to have permanently increased, then rational investors will move from portfolios with more risky assets to portfolios with fewer risky assets.
You probably could have guessed that without all of the curves. If I am comfortable with a certain amount of risk, and the overall risk of things goes up, then it stands to reason that I’d work to reduce my overall risk. The second-order understanding here is, then, that if President Trump is perceived by investors to increase the overall volatility in markets and individual country and company outcomes, we should expect investors to lighten up on equities.
And that brings me to the final chart. This is the Baker, Bloom and Davis news-based Economic Policy Uncertainty Index, which counts the number of articles in US-based news sources that contain a set of predefined terms that indicate uncertainty about economic policy. The dotted lines below show weekly data; the heavy red line shows the 12-week moving average to get rid of the noise.
Notice the three prior spikes on the chart are during and immediately following the end of the internet/stock market bubble in the early 2000s, the end of the housing bubble and the Global Financial Crisis in 2008-09, and the COVID crisis. All three of those episodes were associated with significantly lower markets, although you could argue that harsh bear markets might trigger some policy uncertainty (that certainly happened after 2008). The jump on the right is the Trump jump, and it is already higher than any other period on this chart other than COVID.[2] Volatility we have. Uncertainty we have. And even if you like the President’s policies, the volatility means that we should not be surprised to see investors pull some chips off the table.
[1] If you take this best-returning asset and leverage it, you basically get a straight line going up and to the right forever; the slope of the line depends on the cost of leverage.
[2] Incidentally, the index goes back to about 1985 and although I didn’t show it there are two more bumps that are similar to the leftmost two on this chart: around the 1993 recession, and around the time of the stock market crash in 1987. They are all lower than the Trump jump.
The Effect of Time on Trump’s Win Likelihood
Not everybody is an options trader, but during an election year there is at least one binary option that most of us care quite a bit about and that’s the option on the US Presidency. There are ways to trade the binary option, but my interest here is not in valuation.
People generally understand that if an option with a payoff of $1 or $0 (depending on the outcome of the event) is trading at $0.60, it means that the market is pricing a 60% chance that the event will occur. (Because 60% chance of $1 + 40% chance of $0 has an expected value, if we ignore discounting, of $0.60). But what I think many people don’t naturally understand is how the 60% chance changes over time even if nothing changes in the underlying circumstances.
If you’re not an options trader, this might be confusing. If Trump has a 60% chance of winning based on the current circumstances on July 31st, then if the exact same circumstances prevail on October 31st shouldn’t the odds of him winning still be 60% (and therefore, the price wouldn’t change)? The answer is nope, not at all.
Let’s suppose that we can summarize “the current circumstances” with one metric, that being the national polling margin.[1] Trump currently polls about 2 points ahead of Harris nationally according to the RealClearPolitics average. If that’s still true on November 5th, Trump will win (again, pretending that the winner of the popular vote automatically wins the election). The odds of him winning would be, of course, 100%. If he only drew 49% of the vote, his odds of winning would be 0%. That’s on the day of expiry, when the odds have to collapse to 100% or 0%.
Prior to the last day, time and volatility work in favor of the challenger and against the leader. If I am the leader, then I want nothing to change. Good things will help me, but won’t change the situation (I’m still expected to win), but bad things might change my expected win to an expected loss. The more volatility there is, the more crazy things happen, the more chances there are that my victory will turn to a loss. If I am behind, I want chaos, and the closer I get to ‘expiration’ the more I am willing to risk to get the chaos. Think about pulling the goalie in an elimination round in hockey or soccer…if the team is behind by 1 goal with 1 minute left, then the opposition scoring on an open goal doesn’t change anything – but having an extra man forward has a chance to change the outcome.
Key point: volatility helps the out-of-the-money option. Higher volatility raises the delta (loosely thought of as the chance of ending up in-the-money) of an out-of-the-money option. Similarly, higher volatility lowers the delta of the in-the-money option. This is why there are October surprises.
Time works on options pricing similarly to volatility (fun fact – doubling the implied volatility has the same effect as quadrupling the time to maturity, I the Black-Scholes world). As the expiry of the option approaches, the delta of an in-the-money option gradually rises until it gets to 1.0 at expiry; the delta of an out-of-the-money option gradually declines to 0.0. It’s the same reasoning. With more time to play, there are more chances for good (outcome-changing) accidents to happen to the person who is trailing, and more chances for bad accidents to happen to the person who is leading.
In the context of the election, here’s what this means. (Note: remember this is just an illustration, not a prediction. It’s a pricing model where I’ve made lots of assumptions so as to be able to show this point).
If Trump still has a similar lead in the national polls in two months, his odds of winning will rise – to something like 70%, versus 60% now. After that, it will rapidly go to 100% over the ensuing weeks. And so event contracts will behave likewise…Trump contracts should gradually rise, even if nothing changes, as the opportunities for changes in the race get narrower.
Two more caveats.
One: the option here is not really a European exercise that is determined on November 5th. Since there is such a thing as early voting, the effective expiry is closer. If Trump is leading on October 15th, he’s accumulating actual votes. So it’s really like some kind of weighted average-price exotic option. But the point is, the delta decay will happen faster than I’ve modeled, for that reason.
Two: I’ve assumed volatility is constant. It most assuredly is not constant. Implied volatility ought to rise as we get closer to expiry (October surprise!). That will tend to offset the delta decay that I have modeled.
In summary – don’t take this as trading advice, but as a hopefully useful insight into how deltas (and binary contracts) evolve over time. I hope you found this interesting.
[1] Obviously, we know that’s not right because the US elects Presidents based on the Electoral College process, which is the result of a compromise between those who wanted the President selected by Congress and those who wanted the President selected by popular vote. In recent years, the winner of the popular vote hasn’t always won the Presidency because the most-populous state, California, has overwhelmingly voted Democrat and skewed the popular vote numbers.
Understanding Biden’s Poll Numbers Despite a ‘Strong Economy’
The Biden team keeps talking about how they can’t believe how underwater the President’s poll numbers are, when the economy is so frickin’ good. “As soon as people figure out how frickin’ good it is, they’ll come running to vote for him.”
At some level, one can be sympathetic with that view. Inflation is down to only 3.1%, the Unemployment Rate is still sub 4% even with the most-recent rise, well below the levels when he took office; Average Earnings are up and gasoline prices are down around $3 after being above $5. What’s not to like? Moreover, put this record next to Trump’s record! When Trump came into office, Unemployment was 4.7% and when he left it was 6.7%!
The problem that the Biden team has – and, frankly, the one it has always had – is that they have no idea how actual people experience the economy, and no idea how actual people think.
Americans, on average, tend to be fair. When people think about the Trump years, they recognize that it isn’t quite fair to saddle him with COVID. While they don’t think this explicitly, their memories about the 2016-2020 period fall into “pre-COVID” and “post-COVID” zones. In other words, if in mid-March 2020 a particular consumer was positively disposed towards the Trump economy, then that’s what their memory is. When COVID hit, it started a new time period in their memory. So to the normal person, they remember Trump coming in with a 4.7% Unemployment Rate and watching as it fell to 3.5% in February 2020. “Then COVID hit.” This works against Trump in little ways too; no one gives him credit for the disinflation that happened between March 2020 and the end of his term.
So this is the way that normal people see Trump’s record:
Now, the best part of Biden’s record is that Unemployment fell from 6.7% when he took office to 3.7% as of January. Other than that, though, his record in the minds of Americans looks unimpressive. (Of note is – and folks, don’t shoot the messenger; I’m just showing the data – that the Biden team persistently claims that real earnings have risen during his Administration, while it isn’t so.)
And so now, let’s put them side by side. Inflation is higher under Biden, gasoline prices have risen under Biden, real earnings are down under Biden, and food costs are up (a lot) under Biden. The unemployment rate has fallen more, but is now higher than it was pre-COVID under Trump!
If you realize that Americans are not going to blame Trump for COVID, then it gets very easy to understand why Trump polls better on the economy.
