The Goal of a Optimized Portfolio

As an investor, you want a portfolio that earns as much money as possible with as little risk as possible. In finance, we use a variety of measures that assess returns/risk such as the Sharpe Ratio, Treynor Ratio, Sortino Ratio, and others. In general, the goal is to assess how volatile a stock’s returns are relative to its risk. Let’s look at examples.

SPY, an index that tracks the SnP 500 has realized a total return of 70% over the past 5 years. We can plot a regression line to find that the average daily return is 0.03%. A risk free stock would be one that earns 0.03% everyday for eternity. In reality, stocks do not behave this way, so ideally we own a stock that earns high returns and trends tightly on its regression line with little deviation. One measure of the deviation is called Variance, which is the average distance the actual return deviates from the regression line.

CALM, Cal=Maine which is an egg producer in Mississippi has historical stock prices that resemble a roller coaster. The total return is slightly lower, but due to its spiky nature, its variance and risk adjusted return ratios are much different from SPY.

For reference, I will post the calculations for the relevant metrics, however, the calculations are not important. What is important is that you understand the goal of an optimized portfolio is not only to earn high returns, but to mitigate risk while doing it. If successful, your portfolio worth will increase much more rapidly and you will achieve retirement sooner.

One way to achieve risk mitigation is through diversification.

Check out our post on diversification to learn more.

Another way to analyze returns is through a histogram. As we can see, in general, stock returns hover around 0%.

As we zoom in, we find that the SPY returns are slightly shifted to the right and have more positive return values than negative

However, if we make the same plot for CALM. We find that the returns are more spread out. Yes, there are more largly positive returns, but there are also many highly negative returns. Overall, us investors would agree this stock would be riskier than SPY as the returns are more sporadic.

If we zoom in, we find a very different histogram than SPY. We find the returns are much more evenly distributed and do not seem to tilt negative or positive. This would be another sign that this stock is inherently riskier than SPY.

Of course, this is comprehended in our Sharpe and Sortino ratio analyses, but it is often helpful to visualize the returns to understand what the metrics are measuring.

Formulas:

Deviation= Actual Return – Expected Return

Variance= Square Root ( Average ( Sum ( Squared the Deviations ) ) )

Sharpe Ratio = Total Return / Standard Deviation of Returns

Treynor Ratio= Total Return / Beta

Sortino Ratio= Total Return / Total Period Variance when Return is less than Expected Return

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