Risk Budgeting

Risk budgeting involves looking at individual fund risk and return contributions and then reallocating to maximize portfolio performance. Risk budgeting is a powerful technique because it accounts not only for individual fund performance but also for interaction effects within the portfolio stemming from the dependency structure of the funds.

Implied returns are the result of reverse engineering an optimal portfolio. The portfolio is optimal in the mean-ETL sense, which signifies that the portfolio is using implied returns based on tail loss. Implied returns represent the return a fund must deliver in order to justify the amount of risk it contributes to the overall portfolio. In economic terms, the implied return can be seen as the hurdle rate of the fund given its risk profile. In the maximum STARR portfolio, implied returns and mean returns are equal. It follows that whenever there is a discrepancy between mean or expected returns and implied returns, there is room for improvement. The reallocation rule is: allocate to those funds for which mean return exceeds implied return; and decrease allocations to funds for which implied return exceeds mean return. Following these guidelines will improve the risk adjusted performance of your portfolio.

Risk budgeting is a useful tool because it allows you to incorporate your knowledge of a fund’s liquidity and capacity in your portfolio thereby allowing you to make realistic allocation choices that fit into your current investment policy. These are just some considerations why risk budgeting may be more useful compared to the pure out of the box optimization approach. We usually recommend the use of optimization as a guideline and then reallocating the portfolio based on a well constructed risk budgeting process. There are two ways to quickly select the funds with the best risk budgeting potential. In the data table there is a “Difference” column that shows the difference between Mean Return and Implied Return. The higher the number, the more this fund justifies its risk and can be considered a good candidate for increased allocation. Funds with negative “differences” may be considered redemption candidates. In the table below, Fund_16 would need to have a monthly mean return of 5.58 in order to justify its tail risk. However it only returns 3.47 per month (difference of -2.11), meaning that this fund may be considered for redemption or decreased allocation. On the other hand, Fund_78 only needs to have a monthly mean of 0.5 to justify its tail risk. However since it has a mean of 1.4 (difference of 0.9) you may consider an increased allocation to this investment.

Risk Budgeting

The second way to view this is by using the chart below.

Mean Return vs. Implied Return

This chart provides a visual depiction of the mean return versus implied return concept. The diagonal line represents the STARR optimal portfolio (best tail risk-adjusted return ratio for the entire portfolio). Points above this line (i.e. point 14/Fund_7) represent funds that have higher mean returns than implied returns meaning that their return to the portfolio more than justify the tail risk that they add. These funds provide you with good allocation opportunities. Points below the line are underperforming relative to the tail risk they are contributing.

Investors who are required to select and monitor investment managers should develop a basic understanding of investment statistics. Quantitative tools can provide you with good insight that you can use in your qualitative interviews with managers and when monitoring your investments.