6 Risk Measures I Use When Investing

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Beginner investors often get caught up in the process of picking and adding assets or funds to their portfolios, as well as their performance. This can make them neglect any prudent risk management activities, for instance, because they tend to underestimate their importance. Even more concerning, there is a lot of emphasis on the simplest measures of risk out there, the information about which is essentially available everywhere — including in fund prospects and official documents available online. However, novices often do not realize that risks are not one-dimensional or linear in nature, but rather complex and multi-faceted. So on top of the overused variance and Sharpe ratios, it may make sense to look at some additional measures.

The content of this post does not constitute financial or investment advice. It is intended for information and education purposes only. The author is not affiliated with any institution and does not earn income from any company or financial product that might be mentioned. References to names of institutions are not recommendations.

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1. Skewness and Kurtosis of asset returns

Individual investors may often choose simplicity in their activity and analysis, and that could be the right choice in a lot of instances. But it could also lead to a significant understatement of investment risks. Projection models often assume normal distributions of returns (which can be described entirely by their first moment — mean, and second moment — standard deviation), but that is not the reality. A normal distribution is symmetric around the mean and has a certain peak, but many asset classes over various time horizons (short and long) are unlikely to conform to that shape. For example, if an asset has an actual distribution with fatter tails, that would mean that extreme gains and losses are more likely, which means that the investment is more risky than predicted by a simple normal distribution.

Additional measures I look at, are the third moment — skewness, and the fourth moment — kurtosis. Promotional materials of funds very often do not report these measures. Websites and broker pages or apps allowing you to filter individual stocks, also tend to focus only on the first two moments. But if you want to have a more complete — and useful — picture of the riskiness of an asset or a fund, you need to look at skewness and kurtosis. It also helps you choose the right return (and risk-adjusted return) metrics to apply when assessing performance and whether to include new assets in your portfolio.

A distribution that is positively skewed has a long tail on the right side of the distribution and its mean is typically greater than its median, which is greater than its mode. Since the mean exceeds the median, most of the returns are below the mean, but they are of smaller magnitude than the few returns that are above the mean. Hence, we have limited but frequent downside returns compared with somewhat unlimited, but less frequent, upside returns. For a given expected return and standard deviation, investors should be attracted by a positive skew because the mean return lies above the median. A distribution that is negatively skewed has a long tail on the left side of the distribution, meaning that the few outcomes that are below the mean are of greater magnitude than the larger number of outcomes above the mean. This means that assets with such return distributions will have frequent small gains and a few extreme losses.

Many option strategies result in a skewed return distribution, and many assets have embedded options (e.g., convertible bonds, callable bond grants). Strategies involving portfolio insurance also exhibit skewness. That is why diversified portfolios with such assets or strategies will be impacted by this property.

Kurtosis measures how much the combined weight of the tails of a distribution relative to the rest of the distribution is — the proportion of the total probability that is outside of, say, 2.5 standard deviations of the mean. A normal distribution has a kurtosis value equal to 3, while a distribution with a kurtosis exceeding 3 has wide tails and a tall narrow peak is leptokurtic. This means that a larger fraction of the returns are at the extremes rather than slightly above or below the mean of the distribution. Similarly, a distribution with a kurtosis value less than 3 has thin tails and a relatively flat middle. Hence, relative to a normal distribution, a larger fraction of the returns are clustered around the mean. It is called platykurtic. A distribution similar to the normal distribution as concerns relative weight in the tails is called mesokurtic.

If an asset exhibits a fat-tailed return distribution, then it will generate more frequently returns that deviate extremely from the mean, compared to the normal distribution. If it is thin-tailed, such extreme deviations will be much less frequent. Empirical data show that most equity return series are fat-tailed. Daily currency returns also tend to be significantly leptokurtic. The practical implication of this is that if a return distribution is fat-tailed and we use models that do not account for that, then we will underestimate the likelihood of very bad or very good outcomes. If a certain asset is more susceptible to price jumps, or economic and market conditions produce such price jumps, that typically leads to leptokurtic return distributions.

2. Factor sensitivities

Risk factor exposures are the source of returns in investment portfolios. The way to harvest returns from such factors is to gain exposures to the equity market (i.e., gaining from the equity risk premium) or utilize style factors such as value, volatility and momentum (i.e., style premia). The factors can be numerous and there has been an extensive body of academic research as to how they perform over different time horizons. Professionals usually calibrate regression models in which they construct factor portfolios, representing returns generated as a result of such exposures. The beta coefficients in such models provide estimates of the sensitivities of asset or portfolio returns to changes in the risk factors and can be used to understand the degree to which returns can vary when various market or economic shocks occur.

Regression models need to be correctly specified to avoid incorrect estimations and misinterpretation of results. This requires the right construction of factor premia and the right choice of factors. It is important to keep in mind that different portfolios have different volatilities. This affects the comparability of betas. All else equal, for the same level of correlation, the higher a portfolio’s volatility, the higher its beta. If different volatilities between portfolios are not taken into account, in terms of exposure per unit of risk, the conclusion about which portfolio is more risky may be incorrect.

Even though the example above focuses on some common equity factors such as size, value, volatility, etc., a factor model could be constructed around various types of factors. The model could be macroeconomic — i.e., where exposures to surprises in macroeconomic variables are used to explain returns; it could be fundamental — where fundamental company attributes serve as exposure factors (e.g., leverage, price-to-earnings, etc.); or it could be statistical —e.g., using historical returns of certain groups of securities or portfolios constructed based on some desired characteristics. Hence, interpretation of the sensitivities will be dependent on the type of model used.

3. Kestner ratio

The Kestner ratio (or K-ratio) measures the risk-adjusted return of an investment and the consistency of growth of that return over a given period of time. It serves as a complement to the Sharpe ratio and indicates how steadily a return behaves — the higher the ratio, the better the performance per unit of risk and the more steady the return. The calculation includes:

1. Calculating cumulative returns for each point in time — either summing up arithmetic returns or compounding to obtain geometric cumulative returns. If compound returns are used, a logarithm needs to be applied.
2. Apply a linear regression — regress cumulative returns versus observed returns. The slope coefficient and its standard error are needed.
3. Calculate the ratio of the slope coefficient and its standard error. An adjustment is applied to account for a varying number of return observations and return periodicity. The adjustment factor is the ratio of the square root of the number of expected return observations in 1 year over the total number of return observations.

Unlike the Sharpe ratio, which is insensitive to the order of a portfolio’s period returns, the K-ratio takes into account the order in which they occur. This makes it a better measure of the consistency of wealth creation as it focuses on the trend rather than point-in-time data points, but it is supposed to be used in tandem with measures such as the Sharpe ratio or the Minimum Acceptable Return (MAR) ratio.

4. Company default score

Scoring models are widely used in finance, specifically in measuring credit risk. Such models combine quantitative and qualitative empirical data to determine the appropriate parameters for predicting default. An important technique used for such applications is linear discriminant analysis (LDA) — it estimates a function that helps classify objects (e.g., companies) into groups (defaulted vs. non-defaulted) based on specific characteristics or parameters. The idea of this estimation follows the principle of maximizing the spread between the groups and minimizing the spread within each individual group.

A publicly traded firm’s creditworthiness can be tested with an LDA model developed by Edward Altman — the Altman Z-Score. Generally speaking, the variables chosen for an LDA model are selected based on their estimated contribution (i.e., weight) to the likelihood of default. In the classic form, the Altman model uses 5 ratios: net working capital to total assets, earnings before interest and taxes to total assets, retained earnings to total assets, market value of equity to total liabilities at face value, and sales to assets. The higher the score, the more likely it is that the company will be solvent. Scores usually range between -5 and 20 or above, but cut-off values, which serve as thresholds between the groups. The model has gone through modifications over the years to account for sector specifics, in which case the thresholds can also differ. What is shown in the picture above is one example. Basically, in that example, a score below 1.81 signals the company is likely headed for bankruptcy, while companies with scores above 2.99 are not likely to go bankrupt.

The model is far from perfect — the fact that it relies on financial statement items which can be subject to management and accounting choices, can make it less reliable. It is also much less useful with companies from the financial sector. It is therefore better to be used in conjunction with market-values-based or simulation-based credit default models.

The scoring function can also be converted into a probabilistic measure, offering the distance from the average features of the two pre-defined groups, based on meaningful variables and proven to be relevant for discrimination. A discriminant function is also very useful for performing stress tests based on changes in the key financial ratios. It is important to note that the above estimation is for US equities — the model needs to be estimated on a country-by-country basis.

5. Conditional Value at Risk (CVaR)

The regular Value at Risk (VaR) measures the maximum loss that can occur over a certain time interval with a given level of confidence. It can be calculated from the gains or loss distribution of an asset or a portfolio during that specific time horizon, but it is an incoherent risk measure. The reason is that it only focuses on one part of the distribution and ignores what happens in more extreme cases. Conditional VaR (CVaR) or Expected Shortfall (ES), as it is also known, looks at that tail that VaR ignores and answers the question — how much is the average loss there?

Broadly speaking, more volatile asset classes (such as small-cap U.S. stocks, emerging markets stocks, or derivatives) can have CVaRs many times greater than VaRs. That can be an indication of both higher upside potential and less attractive properties for more extreme environments. The estimation procedure can be somewhat complicated as it requires using the loss distribution — ideally, a simulated one, which can be derived by estimating returns on portfolio positions (or the portfolio as a whole), for instance utilizing factor sensitivities derived from the model described earlier together with a projection of the relevant factors.

6. Concentration risk

Simply using the share of individual or related positions’ exposures in the total portfolio is not sufficient to get a proper gauge of the concentration of a portfolio. A much better way to assess that is to find out how much of the profits and losses (i.e., the returns) is concentrated in a single or just a few names/risk factors/sectors/asset classes/countries, etc. Normally, investors would not mind if profits are highly correlated, in fact, that would be preferred — as long as it does not also mean that losses across these various dimensions of the portfolio are also highly correlated. We definitely do not want that.

Looking at the loss distribution once again, if we know that a significant part of the losses would be caused by just one or a couple of positions or risk factors, that would mean high concentration. One very useful method to assess that is to estimate the Expected Shortfall Contributions (ESC). A position’s ESC is its average contribution to portfolio losses above a given VaR quantile. The higher the contribution in % per given aspect (company, country, industry, etc.), the higher the concentration along that aspect of the portfolio, and hence the higher the risk if something goes wrong regarding that aspect (e.g., mining companies suffering from a regulatory shock).

Conclusion

In this post, I focus on 6 of the main risk measures I use when managing my portfolio. It is important to note, that the goal of this overview is to understand why these are useful in practice and what insight they offer, not to imply that they are comprehensive or sufficient. In that sense, these measures look at some of the often-neglected risk aspects of an investment portfolio, especially by beginners: concentration risk, non-normality risk, factor sensitivities, default risks, and extreme events. Used in combination with other metrics, they can significantly enhance an individual investor’s toolbox and help avoid unnecessary losses.