Value Added Monthly Index – Logarithmic Plot

Hedge Fund Hacks

This is the first post in a planned series about hedge fund quantitative due diligence: “Hedge Fund Hacks“. I will show how to use familiar tools in creative ways to dig deeper into a hedge fund’s returns.

I assume familiarity with the usual gamut of hedge fund performance statistics, but I will provide links to detailed definitions where appropriate.

Value Added Monthly Index

Nearly every hedge fund tearsheet will have a VAMI chart at the top. aiSource has a really nice section on VAMI. Investopedia has a brief definition and a narrative about its use. BarclayHedge has a definition and they provide an interactive VAMI chart for each manager.

The most powerful force in the universe? Compound interest.Albert Einstein (Apocryphal).

All these sources present the Value Added Monthly Index plotted using a linear y-axis. How do returns work? They compound: they do not add, they multiply. While there is no evidence for it, Einstein is credited with saying compound interest is the most powerful force in the universe. If so, we need to be able to see if it is at work in a given manager’s VAMI chart. We can see if a process compounds by plotting it using a logarithmic axis.

The Problem

Here are two randomly generated VAMI curves:

Both VAMI curves have the same return of 12% per year compounded monthly. They also have the same Sharpe Ratio of around 0.5. Both seem to get more noisy from left to right. The increase in noise in the blue VAMI seems greater than the red. The red VAMI seems to curve upwards. Overall though, both these return streams appear fairly similar.

The Hack

We get a clearer picture when we plot using a logarithmic y-axis:

The key feature of a logarithmic plot is that the same percentage change occupies the same vertical distance regardless of the value. I have added a constant rate of return line based on the CAGR and one standard deviation envelopes (dashed lines) so we can visually benchmark the actual VAMI vs. theoretical constant return plus noise.

Analysis

There are two really obvious differences between the Blue VAMI and the Red (remember: same CAGR, same Sharpe):

• The Red VAMI follows a much straighter path up towards the right – what looked like accelerating growth in the linear chart is actually a fairly steady rate of return. The beautiful straight Blue equity curve of from the linear chart is actually a decelerating rate of return. This is quite common among hedge funds, their long run CAGR is impressive due to some strong early years, with performance tapering off later.
• The dispersion of the Red VAMI around its trend line is consistent across the entire curve. Not so the Blue VAMI. The volatility of the Blue VAMI is increasing: The manager is taking more risk for less return.

A more subtle point is that dips in the equity curve across time are comparable now – a dip that visually appears the same size on the logarithmic chart IS the same size in percentage terms – it is much easier to pick out large draw-downs across the entire curve when it is plotted on log-scale.

Extra Credit

A simple trick to confirm our suspicions regarding the Blue VAMI curve is to plot the residuals of the actual VAMI vs. the idealized CAGR line:

There you have it! The residuals are clearly autocorrelated (i.e. the returns are NOT stationary). Secondly the spread of the residuals is increasing over time – the return stream is getting more volatile.

Conclusion

This simple hack of recasting a Value Added Monthly Index using a logarithmic scale for the y-axis yields three benefits:

• Acceleration or deceleration in the rate of return becomes much easier to see – it shows up as an upward curve or a downward curve. On a linear chart the VAMI can curve upward even though the rate of return is decreasing over time.
• Increases or decreases in volatility of returns become much more obvious as constant volatility will now look like constant spread around the VAMI curve. On a linear chart, you expect the spread to increase with increasing VAMI even at constant vol so it’s hard to tell if there is a trend.
• A 25% draw-down when the VAMI was only $1,200 looks just as big as a 25% draw-down when the VAMI is $12,000 – you might not even notice it on a linear chart. This is especially important when looking at very long VAMI charts.

Using the simple hedge fund hack of plotting the Value Added Monthly Index on a logarithmic scale reveals hidden features in a hedge fund manager’s returns.

For additional insights into analyzing hedge fund returns, don’t hesitate to contact us.

Image: Spyglass by tutnh on FreeImages.