Quantitative analysis involves calculating and examining statistics and ratios based on a fund’s historical returns to evaluate performance. The catch, of course, is that past positives are no guarantee of future success. But quantitative analysis remains a very useful exercise: you can assess the return and risk characteristics of individual funds and, crucially, use these metrics to help you choose between several similar options.

It’s sensible to begin by running a quick sanity check of the fund’s previous returns. Look at how long these go back – it’s hard to draw meaningful conclusions from meager information. Investigate whether the same PM and core team has been in charge for all that time too; past performance under a different regime will be a particularly unhelpful indication of what lies ahead. And note too whether the historical returns cited are live or “back-tested”, i.e. simulated. It’s not uncommon for newly launched funds, especially those which invest based on mathematical rules, to cite back-tested returns – but you should always take simulated data with a pinch of salt. 🤏

Let’s turn now to the hard analysis. The first things you want to measure are the fund’s historical average annual return and the volatility this has exhibited. Investors often arrive at the first number by working out a geometric mean that takes into account the effects of compounding. This compound annual growth rate (CAGR) is calculated using the fund’s current NAV relative to NAV either at inception or some other point in time – say five years ago, if you want to assess the fund’s performance over the past five years. Here’s the formula:

Compound annual growth rate (CAGR) calculation

Volatility, meanwhile, expresses a fund’s riskiness based on the extent to which its NAV fluctuates; all else equal, a highly volatile fund carries more risk than one with low volatility. Volatility is best computed using a classic statistical measure: “standard deviation.” To work out the standard deviation of a fund’s historical returns, find the average monthly return across a given time period, subtract this simple mean from each individual monthly reading, square those results, and then find their average. Note that if you’re using monthly returns, you’ll end up calculating monthly volatility – multiply this by the square root of 12 to get annualized volatility.

Annualized volatility calculation

Focusing on annualized volatility allows us to conduct an apples-to-apples comparison with the annualized return measure (CAGR) we arrived at earlier. And that brings us to another metric that’s very often used to assess investment funds: the Sharpe ratio. This measures “risk-adjusted” returns, calculated as the fund’s CAGR divided by its annualized volatility. It basically tells us how the fund performed per unit of risk. Strictly speaking, Sharpe ratios should subtract the “risk-free rate” – the equivalent CAGR of a super-safe asset like short-term government bonds – from the fund’s own CAGR before dividing by volatility. But for the sake of making simple comparisons between different funds, this can be ignored.

Yet another ratio commonly used to weigh up returns against risk is the information ratio. This tracks the fund’s excess returns beyond the returns of its benchmark – usually a market index – compared to the volatility of those returns.

Information ratio calculation

By way of example, take a fund that invests solely in US stocks. Its benchmark might well be the S&P 500 index. To determine the information ratio, we’d first calculate the top part of the fraction: the fund’s CAGR minus the CAGR of the S&P 500 over the same time period. This gives us the “active return.” For the bottom-part denominator, we’d look at the fund’s historical monthly returns and for each month subtract the S&P 500 equivalent. We can then work out the annualized volatility of those excess returns following the process outlined above to arrive at “active risk.” Divide active return by active risk, and you’ve got the fund’s information ratio.

The better a fund’s done versus its index, the higher its excess returns – and the more consistent these are, the lower the active risk. The resulting information ratio is therefore particularly useful at assessing funds that are explicitly benchmarked against indexes – which includes the vast majority of active funds.

The last quantitative computation we’ll touch on is a really important measure of risk called maximum drawdown (MDD). As illustrated below, this tracks the largest peak-to-trough decline in a fund’s NAV. You should generally stay clear of funds that have experienced large MDDs, as this indicates poor risk management by the PM and their team. And knowing the worst loss a fund has previously experienced can be telling: a 50% drawdown, after all, means the fund would subsequently have to double in value just to get back to where it was! 💥

Maximum drawdown illustration

While all these calculations might seem quite involved, the good news is that most of them can often be found included on the funds’ factsheets, or by using the online tools mentioned earlier. Nevertheless, only by knowing how they’re worked out and what they represent can you properly interpret them. When comparing several similar funds, you’ll probably want to lean towards those with higher Sharpe and information ratios and lower MDDs. The best approach is to narrow down a list of candidates quantitatively first – and then analyze the remaining few qualitatively to pick the best one or two.