The Bankers Dozen is a hedged portfolio that measures the preference for idiosyncratic risk and is created as follows:
First, assume that correlation does not result in lower portfolio volatility, so the benefits of portfolio diversification do not exist and total idiosyncratic risk is present. This is compared to a traditional portfolio in which diversification benefits do exist and a portion of idiosyncratic risk has been eliminated. Second, adjust the security weights in the first portfolio, the Bankers Dozen, so the certainty equivalent versus the traditional portfolio is zero.
In other words, structurally, more idiosyncratic risk is present in the Bankers Dozen. Initially, the portfolio is practically the same as the traditional portfolio, because the security weights are identical. However, after optimizing the security weights, investors are not willing to “pay to part” with the added risk, so it is effectively owned. The difference in performance between the Bankers Dozen and the traditional portfolio measures the relative preference for idiosyncratic risk.
This measurement can be compared to the risk-free rate. For example, if investors prefer certainty, they will purchase government bonds, lowering their yields. Likewise, if they prefer certainty, they will have a lower preference for idiosyncratic risk, and the Bankers Dozen will underperform its traditional portfolio equivalent. There should be a general correlation between risk-free yields and the relative performance of the Bankers Dozen.
This concept can be extended to create a risk function that mirrors the risk-free yield curve. For example, the Bankers Dozen has relatively worse performance for larger portfolios. This is because more idiosyncratic risk is present, so the “hurdle rate” for relative performance is higher, and because investors are risk-adverse on average, the hurdle rate is not cleared.
The table below shows, for different portfolio sizes, the average relative monthly performance (in basis points) of the Bankers Dozen over the period of July 1992 to July 2017.
| 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Performance | -0.7 | -2.9 | -3.8 | -4.1 | -5.6 | -6.5 | -8.3 | -9.4 | -8.6 | -10.7 |
Overall, the downward-sloping performance curve is a mirror image of the upward sloping risk-free curve. So, the two functions may be compared to create a rough equilibrium of the quantity and preference for idiosyncratic risk. For example, if rates increase and we assume that quantity is unchanged, then the Bankers Dozen should outperform to restore quantity equilibrium.
The chart below compares the average monthly relative performance of the Bankers Dozen versus average risk-free rates (in percentage points) over the period of July 1992 to July 2017. Statistically, there is not a significant correlation between the Bankers Dozen and the risk-free rate. However, changes in the equilibrium for idiosyncratic risk may be a reason.
From 1993 to 1999, the Bankers Dozen outperformed the risk-free rate, which suggests an increase to both the quantity and preference for idiosyncratic risk. This makes sense, given the preference for specific stocks during the period, i.e. technology. Following the market crash, both the risk-free rate and the Bankers Dozen continually declined until 2004, suggesting that the elevated quantity of idiosyncratic risk was restored to equilibrium.
Then, from 2005 to 2008, the risk-free rate outperformed the Bankers Dozen, suggesting a decrease in the amount of idiosyncratic risk, and implicitly, an increase in the amount of systematic risk. This makes sense, given the broad market crash that followed. Overall, comparing the two risk functions in both market crashes provides some insight, in that the first was marked by elevated idiosyncratic risk, while the second was more systematic.
Since 2008, both risk functions have been relatively stagnant, suggesting a stable quantity and preference for idiosyncratic risk. Meanwhile, the market has performed well, suggesting elevated market premiums. If risk-free rates increase, while the Bankers Dozen performance remains stagnant, then perhaps systematic risk will increase, resulting in a third-market crash. Alternatively, if both risk functions move in tandem, then perhaps we see market stagnancy going forward.
This video reviews the concept of the certainty equivalent using an example of donuts, which is then applied to a portfolio of securities. A series of hedged portfolios are then created to depict a risk function that mirrors the yield curve.