The Lemon Fool

Over the years, I've coded all sorts of little routines to simplify and automate various financial calculations.

Going through some papers the other day, I found some (very rough) pseudo-code for an idea I had back when I was writing regular TMF articles, rather than the bi-monthly 'Collectives' that I do for the site now.

Briefly, I wanted a way to compare two percentage growth rates, so as to be able to say something like "Over the last year, Company X has outperformed the FTSE by Y%".

Company X = +9.91% growth, FTSE = -8.03% growth (ie, negative growth).

Company X = 109.91, FTSE = 91.97, so difference = 17.94.

17.94/ 91.97 = 19.506%

In other words, Company X has outperformed the FTSE by 19.506%.

The reason for posting is that I'm always slightly cautious about comparing percentages, hence the step of turning them into absolute values, eg 109.91 and 91.97. And I also recall the tangles Luni got into with his percentage inflation calculations, which a number of people (myself included) thought were flawed.

So I'd appreciate a second opinion (or two!). Is this calculation conceptually valid?

MDW1954

MDW1954 wrote:Company X = 109.91, FTSE = 91.97, so difference = 17.94.
17.94/ 91.97 = 19.506%
In other words, Company X has outperformed the FTSE by 19.506%.

MDW1954

But by using 91.97 as the denominator, you are using the value at period end. I would have thought that you wanted to use the value at period start.

So 100 in FTSE, left with 91.97; 100 in X, left with 109.91. I'd go for the outperformance being 17.94%, as the amount by which an initial investment in X of 100 outperformed an initial investment of 100 in the FTSE.

The calculation seems valid: in your example, holders of a FTSE tracker would need a 19.5% increase in value in order to draw level with company X again.
I think you can skip the calculation of the difference (17.94) as you get the same result just by dividing the two % values directly (1-(109.91/91.97)).

There is a risk that people will see it as a flawed calculation: dividing a "winner" by a "loser" makes the winner stand out even more. The winner did not give its holder a 19.5% return, but a 9.9% one. The context of the % needs to be very explicit!

VRD

MDW1954 wrote:The reason for posting is that I'm always slightly cautious about comparing percentages, hence the step of turning them into absolute values, eg 109.91 and 91.97. And I also recall the tangles Luni got into with his percentage inflation calculations, which a number of people (myself included) thought were flawed.

So I'd appreciate a second opinion (or two!). Is this calculation conceptually valid?

Yes, had you invested in company X you'd now have 19.506% more than you'd now have if you'd invested in the FTSE instead, so it's absolutely the correct way of looking at it.

I would add though that it's not a figure to look at in isolation, as some fund managers seem to like to do: "This year we had a stellar performance with our fund outperforming the FTSE by 19.5%!" (Fund -12%, FTSE -26.4%)

Doing as you did, and normalizing the amounts (or turning then into actual £ amounts), helps avoid the error that Luni (and others) made/make of simply subtracting percentages from each other. (It's just a shame that, despite being told it was wrong numerous times, by me, you and many others, Luni ignored that and carried on subtracting...)

Thanks, all. That's reassuring. I'll think I'll finally take the next step and turn it from pseudo-code to real code!

MDW1954

MDW1954 wrote:Company X = +9.91% growth, FTSE = -8.03% growth (ie, negative growth).

Company X = 109.91, FTSE = 91.97, so difference = 17.94.

17.94/ 91.97 = 19.506%

In other words, Company X has outperformed the FTSE by 19.506%.

Is this calculation conceptually valid?

MDW1954

Yes, you want the relative return from a growth of X% compared to one of Y%, ie (1+X)/(1+Y) which should then be converted to a growth rate by subtracting 1. So the calculation you need is ((1+X)/(1+Y))-1.

You have calculated (100X-100Y)/(100+100Y).

Now (100X-100Y)/(100+100Y) = (X-Y)/(1+Y) = ((1+X)-(1+Y))/(1+Y) = ((1+X)/(1+Y))-1

So you have calculated what you need. QED

modellingman wrote:

MDW1954 wrote:Company X = +9.91% growth, FTSE = -8.03% growth (ie, negative growth).

Company X = 109.91, FTSE = 91.97, so difference = 17.94.

17.94/ 91.97 = 19.506%

In other words, Company X has outperformed the FTSE by 19.506%.

Is this calculation conceptually valid?

MDW1954

Yes, you want the relative return from a growth of X% compared to one of Y%, ie (1+X)/(1+Y) which should then be converted to a growth rate by subtracting 1. So the calculation you need is ((1+X)/(1+Y))-1.

You have calculated (100X-100Y)/(100+100Y).

Now (100X-100Y)/(100+100Y) = (X-Y)/(1+Y) = ((1+X)-(1+Y))/(1+Y) = ((1+X)/(1+Y))-1

So you have calculated what you need. QED

Thanks, modellingman.

I recall you advising me on a percentage calculation in 1977, and here you are doing the same 40 years on!

This time round, I was happy with the maths, but seeking validation of the concept.

Best wishes,

MDW1954