To get the “free lunch” of diversification in a portfolio, the assets need to be able to move independently from one another—so when one asset zigs, another asset zags. The mathematical measure of how “different” two investments are is called correlation.
Viewing the correlation matrix can help determine if an asset is helping to diversify a portfolio. If an added asset has a correlation of 0.9 to another asset, the two are going to “co-move” most of the time, so the additional asset provides very little diversification. This could inform a decision to remove the asset, or reduce the weight to the asset in order to give more diversifying assets more room.
Most investors prefer to maximize returns while also minimizing risk. Since return without risk is very rare to find, it is helpful to see how the two are related. The chart visualizes the relationship between risk and return to measure how “efficiently” risk is being used. The most efficient portfolio either provides the highest return for a fixed level of risk, or the lowest risk for a fixed level of return. These optimal combinations can be found along the convex upper-left-hand border, called the “frontier”. If your portfolio is close to this frontier, you are getting the most bang (return) for your buck (risk).
Observing a portfolio’s plot (in red) versus a sampling of other weight combinations (in gray) helps to visualize how risk-efficient a portfolio is relative to a range of other possibilities. The position of the portfolio plot can also inform how successfully a weighting algorithm is accomplishing its goal. For example, a weighting algorithm that minimizes variance should be able to plot very close to the farthest left point in the dot plot.
Since risk factors often explain the sources of returns for a portfolio, it is possible to use factor coefficients of a portfolio to disaggregate the source of a portfolio’s returns. This is only meaningful when the risk factors provide good explain-ability (have a high adjusted R2).
Being able to attribute a portfolio’s returns back to fundamental risk factors has many benefits. If a portfolio performed well, but the majority of the returns came from a single risk factor that you don’t feel confident will do well in the coming years, that can help attenuate expectations for future performance. If a portfolio underperformed a benchmark, but under-performance was driven by a factor you have high confidence in the future, that might bolster expectations of performance going forward. This is a useful way to determine if a portfolio is responding to the types of risks you are targeting.
Returns rarely present themselves without taking on risk. Returns that come in exchange for taking on known risks are called risk premiums. A handful of risk premiums do a pretty good job of explaining a portfolio’s returns. We can “regress” a portfolio against these known risk factors to measure how exposed a portfolio is to each one.
Knowing what risk factors you are exposed to can help measure if a portfolio matches your risk tolerances or needs. If a portfolio has a high coefficient to a risk factor that is undesirable, it can prompt a change. Such information can also add conviction in a strategy if exposure to the risk factor is desired.
For portfolios with two or more assets, the amount invested in each asset can vary over time—either due to drift (changes in asset prices), or due to changing the desired allocation (set by the policy). To track the exposure of a portfolio over time, the weight—or percent—invested in each asset is displayed since the portfolio’s inception. Each color represents an asset in the portfolio
The value of the portfolio will change over time, but the weight is always reflected in percentages (so the total adds up to 100%).
Tracking historical weights of a portfolio can help ensure that an investment isn’t overly exposed to a single asset. It also helps visualize the impact of choices such as how often to rebalance, the frequency for updating policy weights, or the preferred weighting algorithm.
A portfolio will tend to have many periods where the returns are slightly above and below the average, and fewer periods where the returns are way above and below the average. If we visualize these periodic returns by plotting how frequently each occurs, we get a snapshot of how common each periodic return is.
Knowing the distribution of a portfolio can help mentally prepare for what the day-to-day reality of living with a portfolio is like. The more fat-tailed a portfolio is, the more “once-in-a-lifetime” experiences you’ll go through. Things that should only happen once every 100,000 years will occur once a decade. A portfolio with high negative skew will look amazing 90% of the time, but then have a devastating loss out of the blue that wipes out most of the gains from before. Negative skew tends to lure investors into a false state of confidence when gains are realized. But those gains aren’t really paid for until the inevitable wipe out hits the reset button. Both excess kurtosis and negative skew can be managed by seeking out diversifying assets. You may even find positively skewed assets to help balance the portfolio out.
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