vendredi 31 janvier 2020

Better metrics - Moving Average & Smoothed Average




Today’s main metric to inform us on how are funds are doing is the Market Value. The Market Value(MV) is highly volatile from day to day. Relying on this metric increase the likelihood of bad investment behavior like selling low, buying high. Also it magnifies, the risk of ruin of the safe withdrawal rule. Most financial planners agrees that one of the key advantage they bring to the table is to make investor stick to the plan. Instead of showing the highly volatile current value of the fund upfront, I suggest to show and use the Moving Average(MA) or the Smoothed Average(SA) as the primary metric.

At a high level, Moving Average and the Smoothed Average are the average of the last years market value adjusted for the time lag. I will explain later in details both metrics exact calculation.

These metrics, MA & SA, have 1 key advantage over the market value, they have lower volatility. Without taking into consideration cash flow both MA&SA produce near identical returns. Therefore, we can safely look at the Moving Average only for clarity at first. Here is a table summarizing the expected 1 year rate of return over the various strategy without cash flows.


Based on historical return (1918-2015) of the S&P 500 and the Moody Seasoned AAA Corporate Bond Yield

We quickly see that the volatility is substantially less in the moving average metric than the market value. The worst years would only affect the Moving average by -7% vs more than triple in Market Value change, -25%, in a 100% equity. That worst variation in Moving Average, -7%, 100% equity is less than the impact on the market value, -11%, at 50% equity/50% bonds portfolio.

If the purpose of buying bonds is to reduce the pain of losing money, why not also take a metric that automatically protect yourself from exuberance of the market.

Here’s a graphic to compare the three metrics through time. The graphics shows the Market Value in blue, Moving Average value in red and Smoothing Average in green (real$) using 100% equity allocation. In order to remove the impact of the ever increasing S&P, I divided each metrics by the average geometric return (7.1%) from 1922. In other word, 1 at 2015 means 631x a fund invested at 1922 (real$). A value of 2 means that the current value is 2x(1+7.1%)^(Yr-1922). At 1930, we can see the MV and the MA are equal at around 1.8. This means that both metric are the same value.

Overall, we can see that the Moving Average return is roughly the same as the Smoothed Average. Secondly, we see that these are reasonable metrics that are about average return like if we were doing the average of the future and the past value. Finally, we do not see the peak that is so characteristic of Market Value Highs and Lows. Instead we notice a smoother ride all along the way.

If we look at the exuberance of the market in 1928, the Market Value was 2.36x above the average return. The Moving Average was 1.64x in 1928. Thus if we were going to show the Moving Average, the investor would have a feeling that he is less rich than he truly is because the market was overwhelmingly hot. Thus, it would have led to a better predictor. Indeed, the irrational investor would have been happier to see a lower decline during the 1930s years than the sharp decline that the Market Value produce. By comparison instead of a drop of 30% over the following years in Market Value, the Moving Average would have a drop of 13%.

Obviously, the Moving Average do not protect against a drop in the market. It only spread its effect. So in the 1970s we see that the market would have drop and drop some more. The MA just trailed behind in the high end during these year, finally to settle to nearly the same value.

These lower drops using Moving Average will help the investor rationalize gain and loss over times. If the purpose of buying bonds is to reduce the pain of losing money, why not also take a metric that automatically protect yourself from exuberance of the market.

The second advantage is that it actually reduce somewhat the risk of ruin using a 4% rule of thumb. For example think of an extraordinary year, using Market value, the 4% rule of thumb would start you withdrawing from the highest peak and thus increasing risk of ruin. Instead using moving average will take a conservative view of the situation and automatically suggest to wait before pulling the trigger. It gives the investor a sense of perspective relative to time as to how well or how poor his strategy returned. However, it is not a silver bullet as much as being flexible in your spending after retirement.

The main disadvantage most widely known against Moving Average is that it hides the current value. Therefore right before the 2008 crash, the moving average would be lower than the market value and right after the 2008 crash, the moving average would be higher than the market value. I would argue that this is exactly the sort of attitude you need to take in order to refrain from doing irrational behavior.

Secondly, you cannot go sale at the Moving Average price. Ex: Market Value = 100$ and the Moving Average = 90$. You will not be able buy at 90$ market share. If you sale at 90$, than you would lose 10$ vs the market value. My counter argument to this disadvantage is that you cannot sale at the displayed market value on your statement that was produce 2 weeks ago at a price tag 1 week earlier. Market is very volatile day to day! Unless you are doing the transaction yourself (go DIY!), you will always suffer a lag. Also, if you are not going to sale the whole funds tomorrow, say 0.33% per months for foreseeable future aka 4% per year, than the price today will only impact a small portion of your wealth. It is not indicative what will be 4% next year or even 0.33% next month.

Currently at January 2020, we are experiencing a somewhat over valued market by perhaps 10%. Using this metric, I would suggest the person waiting to pull the plug to consider some level of conservatism in its estimated net worth and consider it perhaps 10% less than what it is currently. Obviously you would need to redo the math over your own fund to have a more inform consideration.

I hope that I was able to convince you of the usefulness of the metrics. In any case, here is the intricacy of the methodology. 

The Maths

Let’s start by the Moving Average. The Moving Average is a simple technique that simply takes the average of the fund value. In its more common application over a few days or month, we usually do not adjust for expected interest. Our purpose should be to have years to years less volatile portfolio funds value. This is why I would suggest to use the 5 years average. Over such a long period, I would suggest to multiply the result by twice the conservative rate of return. See below example. Using these Market Values, the 5 years average is 263,757$ without adjustment. Then assuming a 6.8% return, we get a Moving Average of 300,848$.

To see the advantage of going with a more complex metric as Smoothed Average, we need to enter some cash flow. After adding some random deposits throughout the years, here’s what the graphic looks like:


Now we can see the advantage of the Smoothed Average (in green). The Moving Average (in red) often drags its feet after we entered cash flow. Conversely, the opposite would occurs if we entered withdrawal instead.

The Smoothed Average is more complex and fits the need where there are any cash flow. Secondly it insert a bias by giving more credibility to the older balance. It will put a credibility of 80% (4/5) over the return 4 years ago, 3/5 over the return 3 years ago, 2/5 over the return 2 years ago and finally 1/5 over last year return. The Smooted Average formula is complex:
SA = MV2017 +4/5*(MV2016+CF2016/2)*(ExpectedRoR-RoR2016) +3/5*(MV2015+CF2015/2)*(ExpectedRoR-RoR2015) +2/5*(MV2014+CF2014/2)*(ExpectedRoR-RoR2014) +1/5*(MV2013+CF2013/2)*(ExpectedRoR-RoR2013).

Here’s a data example with above average return. The Smoothed average would be 298,384$ = 284,067 + 4/5*235,207*(6.8%-21%) + 3/5*264,722*(6.8%-(-11%)) + 2/5*276,271*(6.8%-(-4%)) + 1/5*258,520*(6.8%-7%)

Common adjustment include putting a corridor on these metrics. The corridor will limit the SA & MA between 120% or 80% of the MV. Ideally this corridor is unbiased and reflects the current fund. Other even more complex SA method exist which leads to slightly different average, but in essence this simple SA captures most of what we want.
On the Pros;
  • It fluctuates a lot less than the fund value
  • It delays the immediate impact of a sustain change which leads to lower rash decision
  • It remove unsubstantial change which leads to lower folly decision
  • It reduces the fund in period of high value and increase it in period of low value.
On the Cons:
  • It doesn’t reflect the value of the fund directly. If you would sale the fund, no one is going to give you the Smoothed Value.
  • It lags behind the real curve, if the interest rate is below real average rate of return or is in front of it if using too optimistic rate.
  • It delays sustained change.
  • Huge stress would be recognize over a long period. Thus the impact of the 2008 is felt even in when market were up a few years later.



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Better metrics - Moving Average & Smoothed Average

Today’s main metric to inform us on how are funds are doing is the Market Value. The Market Value(MV) is highly volatile from day to d...