Asset Portfolio Allocation

In this asset portfolio allocation example I will be looking at SPY and BND. Please refer to my previous post to learn about SPY and the benefits we discovered in investing in such a fund. Where SPY is a fund that invests in a broad index of stocks, BND is a fund that seeks to track the performance of a broad, market-weighted index of bonds. Just like how SPY tracks the S&P 500, BND tracks the performance of the Bloomberg Barclays U.S. Aggregate Float Adjusted Index. This index measures the performance of a wide variety of public, investment-grade, taxable, and fixed income securities in the United States. It also includes corporate, government, and international dollar-denominated bonds, and mortgage/asset-backed securities that all have maturities greater than one year. BND holds a broad collection of these securities to basically mimic the entire index.

Now, that we know the backgrounds of SPY and BND, I am going to create 101 portfolios that invest all portions of 100% of my assets between the two. To calculate the mean and standard deviation of the two ETF's, I used the monthly returns from September 2011 to August 2021. The mean for SPY is 1.204% and the standard deviation is 4.437%. While for BND the mean is 0.032% and the standard deviation is 0.908%. Also derived from this data is Rho, the correlation coefficient which comes out to be -5.336%. After creating all 101 portfolios the portfolio that provided the best return based on asset allocation was investing 100% of assets into SPY and 0% in BND. I think this is your best portfolio because as a young investor, return means more to me than risk. So even though this portfolio produces the highest amount of risk, one the risk is still not very high, but two it has the highest returns which is what I am most focused on in this case. I also created an Efficient Frontier based on the 101 portfolios. This can be seen in the link below. The efficient frontier shows the return and the risk for each portfolio allocation.

Efficient Frontier.pdf

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Let's go a step further and add risk free U.S. Treasuries that have a 0.1% monthly return. With these treasuries added I will find the Optimal Risky Portfolio (ORP) out of the 101 portfolios on the Efficient Frontier that was created earlier. Again, with the U.S. Treasuries added the ORP is the same portfolio that we selected above, the portfolio that invests 100% of assets into SPY and 0% into BND, but then this portfolio now also takes into account the 0.1% monthly return from the U.S. Treasuries as well. The Sharpe ratio of this portfolio is 24.87% and to convert that to annual Sharpe I will take the 24.87% monthly Sharpe and multiply by the square root of 12 to get 86.21%. Now, I want to show you how you can create a portfolio on the Capital Allocation Line (CAL) that is better than SPY alone (pictured below). As you can see the portfolio we are creating is the one that is circled that is above SPY's return, but still holds the same amount of risk as SPY. You can construct this portfolio by adding investments in the risk-free U.S. Treasuries. By doing this you are able to receive a greater return while bearing the same amount of risk as investing in SPY alone. Greater return for the same amount of risk? Sign me up!

So far I have created 101 portfolios with different allocations between stocks and bonds and found that the best portfolio is when you invest 100% in stocks. I then went a step further and added in risk-free U.S. Treasuries to show you how to create a portfolio that provides better returns at the same risk as investing 100% in SPY. Cliff Asness, the founder of hedge fund AQR Capital Management, is a huge advocate for allocating your assets 60% in stocks and 40% in bonds. In this section, I will do just that and compare it to the ORP discussed above.

The mean and standard deviation of this 60-40 portfolio is 0.735% and 2.668% respectively. To better compare this portfolio to the ORP I will create a portfolio that is a mix of this 60-40 portfolio and the risk-free asset with the condition that this new portfolio has the same risk as SPY. After calculations it is clear that the 60-40 portfolio mixed with the risk-free assets with the same risk as SPY still does not produce a higher return than if you had invested in just SPY alone. Therefore, we have proven in this case that we should go against Cliff Asness' recommendations and invest 100% of our assets into SPY. This can be explained by looking at SPY's mean and standard deviation and comparing it to all of our portfolios we have analyzed throughout this post. In every case SPY alone has produced a higher return with the same standard deviation as the ORP and the 60-40 portfolios, thus proving over and over again how important it is for us to invest in SPY.

Finally, I am going to add one more ETF to our portfolio to show that we can do better with more than two stocks. To do this I am going to add iShares MSCI Emerging Markets ETF (EEM) which is one of the oldest ETF's that focuses on emerging markets. The index is designed to measure equity market performance in the global emerging markets. The mean and standard deviation over the last 10 years is 0.348% and 5.649% respectively.

I will now create 100 portfolios with random allocations into each portfolio. To create this I used the random function in google sheets to randomize what would be allocated from each ETF. I then took the mean and standard deviation of each portfolio and created a new efficient frontier which can be seen below.

Efficient Frontier (1).pdf

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The portfolio from this exercise with the highest sharpe ratio is from the portfolio with the allocation of 18.21% in SPY, 28.81% in BND, and 52.98% in EEM. This portfolio produced an annual sharpe ratio of 1.103. This is the best sharpe ratio we have calculated in this exercise. This shows how beneficial it is to diversify your portfolios. By having more than just two stocks in your portfolio it allows for more opportunity for your portfolio. If one stock has a bad month, you then have multiple other stocks to rely on to soften the blow. Whereas, when you only have two stocks in a portfolio it puts a lot more pressure on that one other stock to pick up the slack when the other is having a bad month. Therefore, having a diverse portfolio is very beneficial for any investor, and it is something that I strongly recommend having as your advisor.