**Introduction**

In my previous two retirement articles, I wrote about issues related to holding cash as an asset class in retirement accounts, and the links between withdrawal rate, longevity, and asset allocation. Those articles were related to my mobile app Cu Parachute, a Monte Carlo simulation-based retirement income calculator. This article is about the role that risk plays in proper retirement account asset allocation, and is related to a new mobile app I have developed called Allocation. Allocation is a mean-variance portfolio analysis tool which uses annual returns from ten different indices since 1980, performs matrix mathematics, and uses an evolutionary particle swarm optimization algorithm to determine optimal portfolio allocations based upon your personal appetite for risk.

**Retirement Account Questions**

When I began my first job as an electrical engineer, part of the first day orientation involved setting up my 401k retirement account. To set up the account, I was asked to answer three questions; 1) what percentage of my gross earnings would I like to contribute?, 2) to which funds would I like to contribute?, and 3) what allocation of the total contribution would I like to make to each fund? I do not remember how I answered these questions at the time. In hindsight, I believe the first question was the only one with a straightforward answer for my only tax advantaged account: as much as possible up to the contribution limit.

**Risk Posture**

To meaningfully answer the second and third questions, you need to assess the risk posture for your retirement account. This means understanding both the role the account will play in funding your retirement, and your personal investment goals. If you expect to have social security and pension income during retirement, your risk posture will probably be different than if the retirement account will be your sole source of income. Risk posture is also something that is not necessarily age dependent. Two 40-year olds might have very different tolerances for market volatility, and different funding sources outside of their retirement accounts (like a taxable brokerage account of individual stocks, or a rental home). Wealthy retirement account owners may take the position that they only need to get rich once, and wealth preservation is most important. They will want to allocate assets that will provide the lowest risk possible. Some examples of retirement account risk postures include: expecting the highest possible return (no risk aversion), expecting the best return per unit of risk, expecting the lowest amount of risk, etc. The risk posture for your retirement account can change over time and your asset allocations should change as well.

**Optimizing Asset Allocations**

Allocation uses mean-variance portfolio analysis, utility theory, and a powerful particle swarm optimizer to determine the optimal asset allocations for your retirement account based on your individual risk posture. Up to ten indices can be selected for allocation. Each index you choose is meant to represent a fund available in your retirement account which seeks to mimic the performance of that specific index. Also, each index represents a specific asset class (e.g., Russell 2000 represents small market capitalization U.S. stocks). After selecting the indices to allocate, you need to input the risk-free rate of return you would like to use (the minimum expected return from any investment), change the optimization settings to best represent your risk posture, tap the “Optimize” button, and the app will output the optimal asset allocations (see figure 1).

Figure 1 – Example Allocation Screenshots

For the example in Figure 1, I chose four asset classes and input the yield of the U.S. 10-year Treasury Note (from 2/9/2018) for the risk-free rate. I chose to optimize allocations based on the maximum Sharpe ratio to get the best return per unit risk. The Swarm Size and Iterations sliders are additional inputs to the optimization. For this example, the app determined the optimal allocations to be: 19% to S&P 500, 5% to Russell 2000, 1% to MSCI EAFE, and 75% to the Barclays US Aggregate Bond index. Additionally, the results screen shows the portfolio weighted average return (or expected return), the volatility risk (standard deviation), the Sharpe ratio, the portfolio utility, and the inputs to the optimization. The upper right-hand corner of the results screen has a button to save the results for reference.

**Risk Posture Representations**

On the advanced settings screen of the app, the first slider from the top allows you to choose the basis for the optimization. You can choose one of four settings: Max Return, Max Sharpe Ratio, Min Risk, and Max Utility. The second slider from the top allows you to choose a measure of Risk Aversion (and it is only used with the Max Utility setting) (see Figure 2).

Figure 2 - Settings For Risk Posture Representation

The Max Return setting is used for a risk posture with no risk aversion. This setting will allocate 100% of the portfolio to the one index among those you chose which provides the highest average return. The Min Risk setting will provide the allocations which minimize the portfolio’s standard deviation. The Max Sharpe Ratio setting will provide the allocations which maximize the Sharpe ratio:

The Max Utility setting will provide the allocations which maximize the portfolio utility:

where A is a measure of Risk Aversion with a range between 0 and ∞. The app allows the user to choose a Risk Aversion setting anywhere from 0 to 100. Using the Max Utility setting with a Risk Aversion setting can allow you to choose a risk posture anywhere between Max Return and Min Risk. Using Max Utility with Risk Aversion = 0 will provide the same answer as Max Return. Using Max Utility with Risk Aversion = 100 will approximate (but not equal) the Min Risk setting. Using Max Utility with any other Risk Aversion setting will allow you to represent any other risk posture, while the Max Sharpe Ratio will provide the best return per unit risk. The combination of the basis of optimization slider and the Risk Aversion slider can be used to represent your individual risk posture (see Figure 3).

Figure 3 - Example Allocation Screenshots Optimizing On Max Utility With Risk Aversion = 5

Figure 3 shows an example of optimizing based on Max Utility with a measure of Risk Aversion = 5. This example represents a risk posture somewhere in between Max Return and Max Sharpe Ratio. Note how the average return is higher in the Figure 3 example than the Figure 1 example (10.41% vs. 9.13%), while the Sharpe Ratio is lower (0.8280 vs. 0.9044). This is an example of a risk posture where you expect a higher return than you can get by optimizing on Max Sharpe Ratio, but want a lower volatility risk than you would get by optimizing on Max Return (9.15% vs. 16.22% (not shown)). In this way, you can optimize using Max Utility and the measure of Risk Aversion to arrive at the portfolio risk and return which best represents your individual risk posture.

**Conclusions**

Proper asset allocation in retirement accounts is a function of your individual risk posture. This means understanding both the role your retirement account will play in funding your retirement, and your personal investment goals. It is not uncommon to hear suggestions related to retirement account asset allocation like: allocate an equal amount to each fund, or allocate your age as a percentage to bonds and the rest to stocks. These suggestions are unhelpful because they are either too naïve or too imprecise to allow you to make an informed decision. They do not provide you with a measure of expected portfolio returns or volatility risk, and are not tailored to your individual needs. Asset allocation in a retirement account should be optimized to your individual risk posture.

**Disclosure:** I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

**Additional disclosure: **I am trained as an engineer, and am not a financial professional. This article reflects my own opinions and should not be considered financial advice.