What if one of the most elegant ideas in investment theory turns out to be nearly impossible to apply in the real world?
In previous posts, we developed a number of ideas from Modern Portfolio Theory leading to the idea of the Tangency Portfolio.
As a reminder, the Tangency Portfolio is the portfolio which lies somewhere along the Efficient Frontier, and is where a line drawn through the “riskless” rate of return on the Y-axis is just tangent to the Efficient Frontier. Here’s an illustration:
One issue that arises is that as the “risk-free” rate changes, so does the theoretical Tangency Portfolio. In this example, the Tangency Portfolio corresponds to about 60% stock and 40% bonds.
However, if nothing changed except that the “risk-free” rate rose to 5%, the theoretically ideal Tangency Portfolio would jump to perhaps 80% stocks.
The volatility of the “risk free” rate in the real world, by itself, throws into question the practicality of selecting a “risky” portfolio based only on the concepts of the Efficient Frontier and the Capital Market Line.
Tangency Portfolio and a Barbell Strategy
Can we salvage anything useful from the idea of a “riskless” asset and a Tangency Portfolio?
The answer is a qualified yes, but the answer will not be as theoretically beautiful as the pure theory we outlined previously. (Reply to this email and let us know if you didn’t get the previous blog posts but you’d like to receive them.)
We base the answer on three empirical observations about the real world
- There is no truly riskless asset
- The Tangency Portfolio would be frequently (even constantly) changing
- It is costly to adjust portfolios
Let’s unpack each of these observations.
No Riskless Asset
There is no truly riskless asset because there are multiple axes of risk. Not even T-Bills, which are traditionally thought of as “riskless”, are actually riskless.
Why not? Because even if you believe that the probability of the US Treasury paying off all maturing 90-day T-bills on time, in full without restriction in US dollars, you probably understand that the value of those dollars is subject to erosion by inflation.
While the effect of this inflation erosion might be small over a 90-day period, over longer periods, it can be, and has been in the recent past, significant.
For example, for the first 20 or so years of the 21st century, the real return — that is, the pre-tax but after-inflation return — on short term US treasuries was approximately negative 25%. That is, holding the “riskless” asset over this period resulted in losing about ¼ of the purchasing power that you started with.
Tangency Portfolio Changing
As we previously described, even if the efficient frontier were to remain stable, as the “riskless” rate changes, the point of tangency will also change. If we use the 90-day T-bill rate as a proxy for the riskless rate, we see that the Tangency Portfolio would be changing nearly constantly.
Over the long term, the annual standard deviation of the yield on the 90-day T-bill has averaged somewhere in the neighborhood of 3.5%.
On a daily basis, that equates to an average daily standard deviation of about 0.2%. That doesn’t sound like very much.
On a weekly basis, the standard deviation is about ½%, and on a monthly basis about 1%.[1]
Example
Now let’s take a look at how, using some stylized facts,[2] Suppose the riskless rate is 4%. And suppose that we can represent the efficient frontier using the quadratic equation. The Tangency Portfolio is about 60% stocks and 40% bonds, and has an expected return of about 8%.
But if the riskless rate were to fall to 3%, that Tangency Portfolio changes to be only about 52% stocks.
That means that to maintain the Tangency Portfolio, an investor would have to sell over 10% of his or her stock portfolio and switch it to bonds.
On the other hand, if the risk-free rate rose to 5%, that investor would have to sell bonds and buy stocks until his or her portfolio was about 75% stocks.
Efficient Frontier is Sensitive to Assumptions
In the above examples, we have assumed that the Efficient Frontier is known and fixed. But in the real world, it is only ever estimated, and will change with changes in the assumptions.
In theory, to calculate an efficient frontier you’d need to have an estimate for expected return and standard deviation for each asset, and you’d need a covariance matrix for every pair of stocks (or other assets if you’re including other assets).
Currently, there are about 8000 stocks listed on US stock exchanges, and globally an estimated 55,000 stocks.
At 8000 stocks, there are almost 32 million correlations to estimate. That’s a lot of potential for estimation error, and for changes.
When I first began to work with mean-variance optimization models I soon discovered that the models are very sensitive to input assumptions.
Further, and more concerningly, I discovered that the models will tend to heavily weight assets whose expected return is over-estimated, or volatility underestimated, or which are expected to have low correlations with other assets. Thus, the potential for error is magnified.
For example, for many years, it was believed by many analysts (because it had been reported by sources believed to be reliable) that private real estate had about 1/3rd the risk of publicly traded stocks, and a return almost as good.
If you plug that data into a mean-variance optimizer, the model is going to recommend a much higher weight in real estate (maybe even to the exclusion of stocks) than if you had shown real estate volatility using the volatility of publicly traded REITs.
That is a particularly stark example, but it is a valid illustration of the main point. A mean variance optimizer doesn’t “know” anything. And so, it can find that some surprising asset should have a high weight, because the return, the variance, or the covariance is an outlier.
Can the Idea of a Tangency Portfolio Be Saved?
The neatly packaged, beautiful and simple theory of the efficient frontier, the Capital Market Line and the Tangency Portfolio doesn’t quite fit the real world.
Assuming you accept that risk is fully represented by the variance of return (or the standard deviation which is the square root of variance), the model is theoretically sound.
But because implementing on a forward-looking basis relies on forecasts of expected returns, variances and covariances, and because these are hard to forecast accurately on a specific security basis, the model cannot be relied upon to tell us the optimal portfolio. So, can the idea of a tangency portfolio be made useful?
Yes, But.
One central insight of the Capital Market Line might be very useful.
That insight is the idea of implementing a portfolio that consists of a “risky” portfolio and “low risk” holding.
This approach is actually how many famous “value” investors do it. They divide the portfolio into a “risky” part, and a relatively riskless part.
The relatively riskless part is typically cash, or some equivalent short term money market instrument.
This approach may be thought of as a “barbell” strategy, in which there are only two assets – riskless and a single risky portfolio. Marty Whitman told me that’s how he handled his personal investing.
Marty Whitman
Marty Whitman was a well-known value investor who died in 2018 at age 93. I first met Marty when he was in his early 80s. His net worth, as I recall, was in the hundreds of millions.
Whitman had founded Third Avenue Funds. The flagship fund was called Third Avenue Value fund, and focused on investing in mostly stocks, but also distressed bonds, that Whitman and his team believed had exceptional return prospects. The investments also had significant risks associated with them.
I asked Whitman how he invested his own money.
He said that all of it was in his funds, except for a few million dollars, which he kept in what he considered relatively riskless cash equivalent assets.
Warren Buffett
Buffett has publicly stated for years that substantially all his wealth is in his company, Berkshire Hathaway. But as Buffett is the largest shareholder and CEO, that doesn’t mean that Buffett is always 100% long the stock market.
Most of Berkshire’s assets are risky assets – such as the railroad it owns, Mid-America Energy, and the portfolio of stocks.
But Berkshire also holds a ton of cash.
Mutual Funds
Many, perhaps most, actively managed mutual funds also follow this kind of barbell strategy. Their portfolios consist of a “riskless” asset, usually some kind of cash or cash equivalent, and the risky part of their portfolio.
In a future post we’ll look further at choices and decisions regarding the riskless asset for a barbell strategy. In the meantime, click here to request one of our advisor guides.
[1] You may notice that standard deviation does not vary linearly with the period. Variance, which is the square of standard deviation, does, and that is one reason that much of the theoretical work is done with variance, and then adjusted to standard deviation.
[2] When I was in grad school, the professors sometimes like to use the term “stylized facts” instead of “assumptions that make the problem more tractable.” I’m using the term in that sense here.
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