# Portfolio Risk: Let Me Count The Ways!

As we mentioned last week, beauty is in the eye of the beholder in the art world. In the investment business this old saying has a similar meaning. Part of the job for a portfolio manager is to make a good estimate of the future expected returns for a "universe" of stocks and/or bonds. This universe could be very large (there are currently 11,741 stocks available on the TD Ameritrade Institutional platform with a share price greater than $0.00), or very small (the Dow Jones Industrial Average contains just 30 stocks). The other side of the portfolio management equation is the estimate of risk. There are at least a few different measures of security and portfolio risk that are important to consider for the end investor. We will describe the metrics and benefits of estimating systematic risk, unsystematic risk, and downside risk.

## Systematic Risk

Systematic risk is sometimes described as "market" risk. This is because it is the potential danger of investing in the market (stock or bond) as a whole in order to reap the expected rewards of that risk over a long period of time. Most academic research and practical applications use the S&P 500 as the proxy for the stock market, but it could really be any large universe of stocks that attempts to capture the essence of the opportunities available to the portfolio manager. As an aside, a simple analogy for the idea of a "universe" is a fishing pond. We can either choose to fish from a small pond - with fewer potential fish - or fish from a large ocean with a larger number of potential choices. Here are the basic mechanics of estimating the systematic risk of our portfolio.

*B*_{p} = Cov(R_{p},R_{m}) / Var (R_{m})

*B*_{adj} = 1/3 + 2/3 * *B*_{p}

E(R_{p}) = E(R_{f}) + *B*_{adj} * (E(R_{m}) - E(R_{f}))

Beta (*B*_{p}*) *is calculated to be the covariance between our portfolio returns and the market returns divided by the variance of returns for the market. The most common practice is to use 60 monthly returns to determine the covariance and the variance of these returns. This historical beta is usually adjusted using an empirically derived equation to capture the phenomenon showing that over time historical betas tend to wander toward 1.00 - the beta of the market. The last of these three equations is the famous Capital Asset Pricing Model (CAPM) that earned Professor William Sharpe a Nobel Prize in economics way back in 1972. The Es before each variable designate expected returns with the subscripts p, f, and m attached to our portfolio, a risk-free asset, and our market respectively. The 90-day treasury bill is the usual proxy for a risk-free asset, although other maturities could be used.

## Unsystematic Risk

Unsystematic risk is sometimes referred to as diversifiable risk or stock-specific risk. The concept is that choosing just one stock (or bond) for our portfolio introduces a much larger risk than choosing a handful, dozens, or hundreds of stocks (or bonds) for our portfolio. The overall risk in our portfolio is expected to drop with the addition of each security due to the fact that each security tends to have return magnitudes (amounts) and signs (positive and negative) that vary over time with respect to each other. The equation below shows how this works in theory.

S_{u}^{2} = 1/n * S_{avg}^{2}

The unsystematic variance (a measure of risk) in the portfolio is equal to the inverse of the number of holdings multiplied by the average variance across all the holdings. Another way to think about the systematic risk (of the entire market - in this case the S&P 500) is to think also of the variance rather than betas. During the last 60 monthly return periods, the S&P 500 had a variance of 0.0020. When taking the square root of this variance, we get a monthly standard deviation of 4.47%. Multiplying by the square root of 12 (for our 12 months in each year), we are left with an annualized standard deviation in returns for the S&P 500 of 15.47% over the past five years.

The smoothing effect from adding securities into a portfolio can be seen in the chart shown below. The "asymptote" of adding a large number (n) of securities is the risk of the market. One might wonder: why not just add all the securities in the "market" into our portfolio? This is exactly what an index mutual fund or an index-tracking exchange traded fund (ETF) does for a small management fee. There are three main reasons why this may not be the best idea.

- Not all securities in the market have the same expected returns. We may expect some to have negative returns over short or long periods of time.
- It can get very expensive to add all the securities in the market into a portfolio due to explicit (commissions) and implicit (spreads) trading costs.
- The complexity of adding a large number of securities can pose a trading and taxation nightmare for an average investor.

## Downside Risk

Downside risk is the most raw form of risk - or emotional pain - felt by the investor. Is is the measure of "how much can I lose" in a portfolio or investment strategy. My late grandfather (on the Rice side) lost 90% of his portfolio in the stock market crash of 1929. He was very fortunate that his sister did not take on as much risk and was able to bail him out of his predicament. For some, downside risk (otherwise known as drawdown) can have a massive impact on our short term wealth as well as a crushing blow to our confidence. One of my clients - a millennial - was very concerned in early 2019 when the market (as defined by the S&P 500) took a nearly 20% drop. We reassessed their personal risk tolerance, realigned their portfolio, and everybody lived happily ever after.

The chart below shows the drawdowns experienced by the S&P 500 over the past 25 years. While the 2019 drop was disturbing, the dive in early 2020 was both quicker and deeper. How quickly our world changed in mid-March! These two drawdowns certainly took our breath away, but the rebound back to the "surface" was fairly quick each time. The bear markets of 2000 and 2008 painted a much graver picture. Not only were they deeper drops (some joked that their 401(k)s turned into 201(k)s), but they lasted much longer in time. The drop and recovery clocked in at 3+ years and 2+ years for the second. The biggest challenge we humans face is that there is an emotional connection between our money and our perceived self worth. One of the most important questions to ask a client is: When do you absolutely need this money? To rephrase the question in less polite terms: How long can you stand feeling completely stupid before you look incredibly brilliant? This is the most important question a portfolio manager can ask you. If the answer is less than a full "market" cycle, then an allocation to stocks of less than 100% is probably a very good idea.

*Source*: Kwanti

Here we introduced three different risk measures and tried to show how they are different and yet complimentary in the toolkit for a portfolio manager. Past performance is - of course - no guarantee of future results. Next week we will talk more about risk tolerance. Stay tuned!