Portfolio Risk Measures
Evaluating Measurements
A trading portfolio is an accumulation of several assets each with its own payoff profile. Risk is a measure associated with volatility, meaning the chance of losing a certain proportion of your investment. Understanding the risk profile of a portfolio can be crucial to determine the weights and makeup of it.
Risk measures can be classified as absolute measures and relative measures, however both aim to quantify the level of uncertainty in the outcomes of a portfolio.
Alpha
Measures risk relative to a benchmark index. A positive alpha means the portfolio outperforms the benchmark, and a negative alpha means the portfolio underperforms the benchmark. It is a risk-adjusted measure, as it takes the volatility of a portfolio and compares the risk-adjusted performance to the benchmark.
Beta
Beta is a relative measure of the volatility or systematic risk of a portfolio to the market or a benchmark. A beta of 1 represents a perfect match between the two, and any beta higher than 1 suggests the portfolio has higher volatility than the market. A beta of less than 1 is seen when a portfolio has lower volatility than the market.
There are some issues with beta as a risk measure, notably it relies on historical information rather than future expectations. In addition, it is focused on fluctuations rather than absolute losses, which can be detrimental when losses are persistent however with small oscillations.
Standard Deviation
Arguably one of the most widely used risk measures, this aims to measure data dispersion relative to the mean value of the dataset. This provides insights to portfolio volatility, a useful estimate for risk management. It tells us how much investment returns are deviating from the average returns.
There are distributional issues of returns to consider which is a drawback of this measure, as it assumes all assets, portfolios and benchmarks follows the same distribution, which is a harsh restriction to make.
Sharpe Ratio
This represents the risk-adjusted return of a portfolio, or in other words, how much return is earned for each unit of risk taken on. A positive ratio means that a particular assets or portfolio outperforms the risk-free asset, and if the ratio is negative it means the risk-free asset outperforms the portfolio.
Risk-free assets are generally considered as Government bonds, due to the ability of the Central Bank to print as much money as possible (in theory) and so be able to pay all debt it owes (in the form of bonds). However, in reality Central Banks are constrained by inflationary pressures to limit printing of currency, and so there exist no true 'risk-free' asset. Government bonds serve as the best proxy.
Again, this is subject to distributional assumptions which do not hold in reality. There is truly skewness in returns which distort the Sharpe ratio.
VAR
Measures the chance of extreme loss in the value of a portfolio over a certain horizon, for a given confidence level. In other words, a 1% VAR would tell you in 1 in every 100 you expect losses below a certain cutoff (VAR).
There are problems with manipulation of VAR, as portfolios may be broken up into the individual assets and shown to have less risk than the combined portfolio, which is misleading. In addition, this measure fails to identify losses beyond the VAR cutoff, and so cannot distinguish between a case of a loss of 1% over VAR vs a loss of 50% over VAR.
Treynor Ratio
Known as the reward-to-volatility ratio. It measures the excess return obtained from taking on one extra unit of volatility. The excess return refers to return over an equivalent sized investment in a risk-free asset. Volatility in the Treynor Ratio is measured using beta. A higher ratio is more desirable.
While a good indicator of risk, it faces some limitations, notably it is backward-looking, and also we can determine that one portfolio may be 'better' in terms of a higher Treynor Ratio, however we cannot judge by how much it is better.