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By defintion, doesn't the Sharpe ratio use a denominator that is the risk, and that is the risk that's taken up until right now, and if only the risk changes and nothing else, the ratio for an investment will change?

If that is true, can I argue that it is a misleading measure of the investor's competence because the investor can only be expected to know the risk at the time of the purchase? Therefore the risk that should be used in the Sharpe ratio should be the risk at the time of investing and not change afterwards. Do you agree? I mean if we look at a portfolio and the Sharpe ratio is high or low, we draw the conclusion that the investor is good if the Sharpe ratio is high and likewise, but in fact, it will be misleading and the right measure to show who is a good investor would be to use the return in the numerator of the ratio (as usual) and the risk that was taken at the time of the investment in the denominator, which may very well have been in 1987 or 1914 for an investment that was bought and then hold and a long time. It should be the available risk taken for the investor at the original point in time when the investment was made. Do you agree?

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    $\begingroup$ In a sharpe ratio context, what's being calculated in the denominator is the standard deviation of the return that's in the numerator. So, if you want to call it risk, that's fine, but the standard deviation of the return is an unknown parameter and it's being estimated by the formula used in the denominator. $\endgroup$
    – mark leeds
    Commented Oct 30 at 6:26
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    $\begingroup$ When is an investment decision made? If you bought a stock yesterday and you continue to hold it today, are you making a decision to stay invested or not making a decision at all? $\endgroup$
    – Rylan
    Commented Oct 30 at 8:47
  • $\begingroup$ The ratio you are computing is the ex-post Sharpe ratio, also known as the historic Sharpe ratio, it is not what the investor was caring about at the beginning of the investment years ago which would be the ex-ante Sharpe ratio; unless the investor wrote down at the time what he estimated it to be it is unknowable. $\endgroup$
    – nbbo2
    Commented Oct 30 at 8:51

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If I understood your question well, what you are actually asking is this -

What is the correct way (in terms of lookback horizon) to measure the "true" Sharpe based on the performance of the portfolio manager?

This query (in my opinion), helps to resolve the dispute well: Portfolio rebalance - How many data back do I need to perform sharpe ratio optimization

Measuring the Sharpe of an asset or a PM is not that much different as a PM is just a compilation of assets. The query above talks about how to estimate the "true" Sharpe based on how far back the lookback horizon.

I personally do not think it makes sense to measure the performance of a PM based on the time of investment to the current date. This is because, as the query and as @phdstudent answers - you need a hell of a long lookback. Therefore, if you want to measure the performance of the PM from the investment to the current date, a good Sharpe could just be due to luck.

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  • $\begingroup$ "a good Sharpe could just be due to luck" is exactly what I see right now. My portfolio's Sharpe ratio is almost 4,0, looking like I am somebody who knows what I'm doing but it's because I was YOLOing and bought a lot of Bitcoin in 2022, then got lucky during the recent rally. It gives the wrong impression when I show my Sharpe ratio that is close to 4,0. It looks like I have been making extremely well-founded investment decisions based on careful analysis and risk-taking, when the truth is that I was buying Bitcoin just because I believed in it. $\endgroup$
    – Niklas Rosencrantz
    Commented Nov 13 at 2:36
  • $\begingroup$ @NiklasRosencrantz exactly. It takes a really long lookback to make an informed decision, which is why measuring the performance of a PM using a short horizon makes no sense. $\endgroup$
    – KaiSqDist
    Commented Nov 13 at 9:19

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