Value-at-Risk (VaR)

Value-at-Risk (VaR) is a measure of the downside risk (exposure to loss), which an individual investment or portfolio holds.

VaR is based on three components: a percentage loss amount, a confidence level and a time frame. It can be calculated for a set of historical data by looking at the actual returns and putting them in order of worst to best.

VaR answers the question "what is the loss that will not be exceeded over the next year with a probability of 95%?". In other words, in 19 out of 20 years an investor would expect either positive performance or a loss up to the level described by the VaR. This means it is possible that your portfolio value could decline within a given year by more than the VaR of your portfolio, but the likelihood for this to happen is only a 1 in 20 chance.

Risk adjusted return

Risk adjusted return measures how much return an investment made in relation to the risk that was undertaken to achieve that return.

If you compare returns of different investments in isolation the results can be misleading. For example – Investment A returns 5% over a 1 year time horizon. Investment B returns 4% over the same period. With no additional context one would assume that investment A is preferable. However, if you also know that investment A dropped 15% in the first 6 months and then recovered 20% in the remaining 6 months whereas investment B rose a steady 1% every 3 months throughout the year: which investment would you prefer to take next year?

Risk-adjusted return allows for a direct comparison of returns between investments. Also, it allows for a direct return comparison to the benchmark.

Downside risk

Downside risk is the financial risk associated with loss or the risk of the actual return being less than the expected return.

Downside risk measures quantify the “worst case” scenario for an investment or how much an investor stands to lose. Some investments have a finite amount of downside risk, while others have infinite risk.

Downside risk measures help investors make proper decisions when faced with abnormal return distributions.

Sharpe Ratio

The Sharpe ratio is a measure frequently used to determine risk-adjusted returns and is commonly defined as the average return earned above the risk-free rate of interest, divided by a portfolio’s standard deviation, which is a measure of its risk level.

Since a portfolio’s performance is measured by looking at its return above the risk-free interest rate, the Sharpe Ratio assesses how effective the risk-taking activities of a portfolio manager or a fund manager were in relation to the additional risk that was added to the portfolio in order to produce those incremental returns.

While the Sharpe Ratio has become very popular as a way to standardise performance measurement across portfolios exhibiting different levels of risk, its main shortcoming is its use of the standard deviation (the square root of variance, also called volatility) as a risk measure.

Critics point out that most portfolios contain assets that don’t have distribution functions behaving according to a normal distribution; instead, their distribution functions have so-called ‘fat tails’ or a negative skew, implying that large deviations from the mean are more frequent than a normal distribution would predict, particularly on the downside. The Sharpe Ratio doesn’t account for this empirical observation. Additionally, the Sharpe Ratio should not be used when looking at assets with non-linear risk such as options, swaps or warrants.

What’s the practical use of the Sharpe Ratio for retail investors looking for guidance as to where and how to invest their money?

The Sharpe Ratio can help you understand if high absolute historical returns on a certain investment (e.g. an actively managed equities fund) have been the result of an intelligent investment methodology, or if the investor was exposed to very high levels of risk in order to achieve those returns. The reason the level of risk is so important is that if the investor was exposed to high levels of risk then the potential for large negative returns is also greater. If the Sharpe Ratio of a portfolio is low (e.g. less than 0.3) then the investor knows that relative to a portfolio with a higher Sharpe Ratio (e.g. 0.5), they would be exposed to greater risk, and therefore greater potential losses, in order to achieve the same level of return.

**Sharpe Ratio = (rp – rf )/ σp**

where,

rp = Portfolio return

rf = Risk free rate

σp = Portfolio standard deviation

Risk-free rate

The risk-free rate is the theoretical rate of return for a risk free investment.

The risk free rate is aligned to the central bank base rate for the relevant jurisdiction (e.g. Bank of England in the UK) and the closest investment to a risk free investment is often high quality government bonds (e.g. GILTs in the UK). In reality even a government bond is subject to a very small amount of risk.

The risk free rate provides a consistent benchmark against which other investment can be compared.

Risk tolerance

All investments carry a degree of risk. Each investor must consider their own personal circumstance and conclude how much risk they are prepared to take on. Failure on an investor’s part to fully consider their own circumstances and tolerance can severely damage any return on investment as it may result in investors pulling out their money when the market is not at an optimal level for them to do so.

Investors can work out their risk tolerance by taking questionnaires, online or with a Financial Advisor, which factor in influences such as investment time horizon, earning capacity, current assets and what you are saving for.

Risk/Volatility Clusters

Empirical data demonstrates that periods of high or low volatility occur in clusters. In other words there is a correlation between volatility from one day to the next. If the markets observes a large move today then there is a greater than 50% chance that tomorrow will also bring large market moves. We call these periods where we observe continued high or low volatility, risk clusters.

Expected shortfall

Measuring the market risk of a portfolio can be done is several ways. One such way to measure financial risk is using a concept called Expected shortfall.

Expected shortfall is similar to Value at Risk in that it measures potential losses in a portfolio however Expected Shortfall focuses more explicitly on the losses which occur within the tail of the distribution. Expected shortfall is also called Conditional Value at Risk, Average Value at Risk, and expected tail loss.

Expected Shortfall is a conservative risk measure focusing on the expected return in the worst X% of a distribution. For example the average loss in the worst 5% of outcomes of a portfolio may be -10%. So in this case the expected shortfall at the 5% level is -10%.

Expected shortfall has attractive theoretical properties in that it “looks beyond” Value-at-Risk by focusing on the tail of the distribution, but it has the disadvantage that in risk and allocation models it is difficult to empirically validate. For this reason and due to Scalable Capitals use of linear, derivative free asset universes, we use the risk measure Value-at-Risk to manage the risk in our portfolios.

Unsystematic risk

Unsystematic risk is company- or industry-specific uncertainty that is inherent in each investment which can be reduced through diversification. It is also known as ‘specific risk’, ‘diversifiable risk’ or ‘residual risk’.

For example – if you hold an investment in a car manufacturer, then if the employee union went on strike, it is likely that the value of your investment would be affected. This type of risk is known as unsystematic risk because it is specific to the investment you hold and could be reduced/removed through diversification.

Sortino Ratio

The Sortino Ratio is similar to the sharpe ratio in that it gives the amount of return generated for a particular investment in the context of how much risk was taken to achieve it. The difference however, is that it only takes into account downside deviations. The Sortino Ratio is calculated by subtracting the risk free rate from the returns of a portfolio and then dividing by the downside deviations. The larger the ratio, the lower the probability of loss.

When deciding when to use the Sharpe Ratio or the Sortino Ratio the investor’s main choice is whether they want a standard deviation based measure or a downside deviation measure. For portfolios with high volatilities the Sortino ratio can add value as a risk measure as it accounts for potentially large negative movements in the portfolio.

**Sortino Ratio = (rp – rf)/ σd**

where,

rp = Expected Return

rf= Expected rate of return

σd= Standard Deviation of Negative Asset Return