Long-dated Calls

Stocks A to Z
21

I believe this approximation (as I understand it) works well only when there are lots of trades (of somewhat short period in between them) in and out of the portfolio.
It fails when the holding period between the “in” and “out” is long.

It becomes almost a philosophical question determining how many dollars you have committed to something–how much capital you had committed and at risk and for how long.

Say you check your portfolio on the last day of every month, and only on that day.
You look at all your positions and decide on your capital allocation for the coming month and do any trades you deem prudent.
Let’s say you decided you wanted to own 500 shares of XYZ and bought them.
You don’t look at your portfolio again for a month. You have no idea what the prices did during that stretch.

How much capital did you have at risk in XYZ that month? How many dollar-days of commitment did you make to it?
Was it the amount of hard earned cash you put into the position, or the average monthly market value of that holding that you never looked at?

Different people look at it different ways.
To me, the “capital at risk” of a position is its market value the last time you looked at it and were willing to consider a change to the position (whether you traded or not).
In essence, the value at the most recent moment that you decided on how much capital to commit.
It might have spent a lot of time since then worth more or less, but you didn’t choose those numbers to allocate to it.

For those who believe this method makes the most sense, my rate of return calculation is precisely correct, not an approximation.
It just depends on what you mean by having capital at risk.
Is it what you decided to put into the position when you opened it, or the market value at some later date?
Does the answer to that question depend on whether you knew the price on that later date?
Different people presumably find different calculations more insightful.
To me, it’s all about the return on the capital you decided to commit.
By extension, the denominator is unchanged by market price fluctuations between portfolio review dates.

So, in your “one dollar for ten years” example, to me you can’t calculate a meaningful rate of
return on time-weighted capital at risk unless and until we know whether the investor
(a) looked at the portfolio periodically in the mean time with an eye to perhaps reallocating the capital, or
(b) just went away for half a Rip Van Winkle.

Jim

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22

@mungofitch wrote:

So, in your “one dollar for ten years” example, to me you can’t calculate a meaningful rate of
return on time-weighted capital at risk unless and until we know whether the investor
(a) looked at the portfolio periodically in the mean time with an eye to perhaps reallocating the capital, or
(b) just went away for half a Rip Van Winkle.

Actually this is incorrect as IRR doesn’t depend on how often one looks at the portfolio w/o doing anything. For any investment, IRR depends only on (1) the timing of capital transactions “in” and “out” of the investment, and (2) the total length of investment period. Wikipedia does a good job of defining IRR: https://en.wikipedia.org/wiki/Internal_rate_of_return

In my example, 7% is the correct IRR and it is a function of only when the money went in and out ($1 went in and $2 came out at the end), and the length of investment (i.e., 10 years).

However, to make your calculation give the correct answer to IRR, one is forced to look at her portfolio quite often even if she plans to do nothing at those intermediate times just so that she can calculate profit at those intermediate times and update the capital at risk to reflect its market value at those intermediate times.