How to chart a risk/return scatter

A risk/return scatter puts annualized volatility on the x-axis and annualized return on the y-axis, and plots one point per fund, strategy or asset rather than one point per date. Up is better, left is better, and the diagonal running from the risk-free rate through any point is that point's Sharpe ratio. Two decisions do most of the damage in practice: which return you put on the y-axis, because the compound rate and the average of the periodic returns can rank the same funds in opposite orders, and whether every point covers the identical window at the identical frequency, because if they do not the chart compares nothing.

One point per fund, not one point per date

Almost every other chart in a performance pack is a time series. This one is the cross-section. It collapses a whole track record into a single pair of numbers so that a dozen track records can be looked at together, which is exactly what it is for and exactly where it misleads. A fund that ground out its return steadily and a fund that made all of it in one quarter and then went sideways can land on the same dot, because standard deviation does not care about order. Show the scatter next to the underwater drawdown curve and a rolling Sharpe line, which describe the same risk through time, rather than letting one dot per manager stand on its own.

Annualize both axes, and say how in the caption

Volatility is the standard deviation of the periodic returns multiplied by the square root of the number of periods in a year: root 12 for monthly returns, root 252 for daily, root 4 for quarterly. Return is the compound annual growth rate, the ending value over the beginning value raised to the power of one over the number of years, minus one.

Both of those carry an assumption worth stating on the chart rather than in a footnote. The square root scaling holds only if returns are independent from one period to the next, and the annualized volatility of the same fund measured from daily data is routinely different from the number measured from monthly data. Illiquid or appraisal-priced strategies look calmest of all at low frequency, because smoothing suppresses the very dispersion the x-axis is trying to show. If your funds are not all sampled at the same frequency, fix that before you plot, not after.

The y-axis choice that flips the ranking

This is the mistake that survives review, because both numbers are called the return. Take two illustrative funds over three years. Fund A returns 12 percent, 11 percent and 13 percent. Fund B returns 60 percent, then loses 35 percent, then gains 30 percent.

Average the yearly figures and Fund B wins comfortably: 18.33 percent a year against 12.00 percent. Compound them instead and the order reverses. Fund A turns 1.00 into 1.4048, a compound rate of 12.00 percent. Fund B turns 1.00 into 1.3520, a compound rate of 10.58 percent. The fund with the higher average return ended with less money, and on a scatter drawn with average returns it plots above the fund that actually beat it.

The gap between the two is roughly half the variance, which is why it widens with volatility and is invisible for a steady fund. Since the x-axis of this chart is volatility, the error is worst precisely where the chart is trying to say something. Plot the compound rate. If a mandate requires the arithmetic mean somewhere in the pack, put it in the table, not on the axis. These three-year figures are a clean illustration of the arithmetic rather than a live track record, and three annual observations are far too few to estimate a real volatility from.

Sharpe is a slope on this chart

Excess return divided by volatility is exactly the gradient of the line from the risk-free rate on the y-axis to the point. With a risk-free rate of 4 percent, a fund at 8 percent volatility and 10 percent return, a fund at 16 and 16, and a fund at 4 and 7 all sit on the same ray and all have a Sharpe of 0.75. Drawing two or three of those rays across the plot turns it from a picture into a reading: anything above a ray beats that Sharpe, anything below it does not, and a fund far out to the right can sit on a better ray than a quiet one near the origin. Label the risk-free rate you used, because moving it rotates every ray. The Sortino and Calmar versions of the same idea change the denominator, so they cannot be read off this chart's geometry.

A scatter of realized points is not an efficient frontier

The two charts look alike and mean opposite things. A frontier is forward looking and constructed: it is the boundary of what a set of assets could have produced under an optimizer, given expected returns and a covariance matrix. A risk/return scatter is backward looking and observed: it is where specific funds actually landed over one specific window. Fitting a curve through the upper left points and calling it a frontier turns a description of the past into an implied promise about the future, and it is the single most common way this chart gets misused in a pitch deck.

If the question really is about combining these funds rather than ranking them, the scatter cannot answer it, because it contains no information about how the funds move together. That is a correlation matrix question, and two funds sitting on the same dot can behave completely differently inside a portfolio.

If you size the bubbles, size them by area

Sizing points by assets under management is a genuinely useful third dimension, and it is usually drawn wrong. The eye reads area, so the quantity has to map to area rather than radius. A fund with 2 billion under management next to one with 500 million is four times the size, which means twice the radius, not four times. Set the radius proportional to the square root of the value and the picture stops shouting. Also cap it: one giant bubble that swallows three neighbors has stopped being a data point.

Make the points comparable before you plot them

Four checks, all boring, all worth doing. Every fund covers the same start and end date, so a manager who launched two years into a five year window is either excluded or clearly marked. Every series is sampled at the same frequency. Every return is measured the same way on fees, either all net or all gross, and the chart says which. And the universe includes the funds that closed, because a scatter built only from survivors is an advertisement rather than a measurement, and the point it drops is always in the bottom right.

One more, if the funds report in different currencies: convert first, and say whether the returns are hedged. An unhedged conversion moves both the return and the volatility of every point, and it moves them by different amounts.

[QUADESTO-EMBED: risk/return scatter, annualized volatility on x against compound annual return on y over a common window, bubbles sized by AUM area, two iso-Sharpe rays drawn from the stated risk-free rate, hover shows window, frequency and net or gross]

Building it in Quadesto

Give Quadesto a set of return series and it aligns them to a common window and frequency first, then plots annualized volatility against the compound rate, sizes the bubbles by area, and draws the Sharpe rays from whichever risk-free rate you name, with the window, the frequency and the fee basis printed on the chart rather than assumed. The free tier embeds it live with a Made with Quadesto credit; Pro at 149 pounds a month removes the attribution and adds branded themes for a factsheet or a quarterly letter.