# Statistical Analysis of Stock Performance

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Hi All,

I'm trying to figure out a way to evaluate my portfolio's performance statistically, taking the idea that if you want to do something, you should probably measure it.

I have the problem of having switched from a portfolio of mutual funds to stocks over time as I've learned more. This creates a challenge evaluating my performance as the portfolio wide metrics are not appropriate (i.e. I'm fully aware that my mutual funding picking skill is shit).

So, I have records of each stock I've bought (when, how much, etc) and I've created a paper benchmark for each stock using a paper-traded portfolio of ETFs (i.e. if I bought 100 shares of AAPL on the Jan 1, 2016, I create a paper trade of VTI for the same dollar amount on the same day). This gives me a dollar-weighted benchmark for each stock, meaning that the IRR of each stock can be compared to the IRR of its benchmark. The difference between these two numbers can be thought of my "alpha" for the stock.

B/c's these "alphas" are independent(-ish) samples, I want to test them statistically. I think it's appropriate to weigh the alphas by age, (specifically, a "money weighted age" or, log base(1+IRR)[Gross Return] = age) The t-test isn't appropriate, but I think I sign-rank test is fine.

I'm not sure on the statistical test, but I'm not aware of a more appropriate model (quick Googling turned up nothing useful). If I do this, I get something reasonable, but any feedback/comments are appreciated

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What are the exact hypotheses that you want to test?

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What are the exact hypotheses that you want to test?

Does the aggregate return (IRR) of the stocks I choose differ from chance. I can't figure that one out so I've settled for does the distribution of returns for individual stocks differ from chance.

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What are the exact hypotheses that you want to test?

Does the aggregate return (IRR) of the stocks I choose differ from chance. I can't figure that one out so I've settled for does the distribution of returns for individual stocks differ from chance.

In an ideal scenario,

1) You compute the mean and variance of your individual stock returns.

2) You compute the mean and variance of the S&P 500 individual stock returns.

3) Compare the two distributions using t-test or another appropriate test based the characteristics of the distributions.

I don't know an easy way of performing 2), though. There must be a data service (Bloomberg?) where you can obtain the return of individual stocks for a given time period?

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What are the exact hypotheses that you want to test?

Does the aggregate return (IRR) of the stocks I choose differ from chance. I can't figure that one out so I've settled for does the distribution of returns for individual stocks differ from chance.

In an ideal scenario,

1) You compute the mean and variance of your individual stock returns.

2) You compute the mean and variance of the S&P 500 individual stock returns.

3) Compare the two distributions using t-test or another appropriate test based the characteristics of the distributions.

I don't know an easy way of performing 2), though. There must be a data service (Bloomberg?) where you can obtain the return of individual stocks for a given time period?

Ideally what I'd do is compute a distribution IRRs over paper traded portfolios of randomly selected stocks. I'm generally not a huge fan of parametrics.

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I am not very good in statistics, but it seems to me that what you described in first post is very different from what you described in the last one.

To deal with the last one:

- You know your own IRR and your cash inflow / outflow times and amounts.

- Build a model that buys/sells random stock to satisfy inflows/outflows. Also buy/sell at random other points within timeline (you can adjust trade frequency). You can also adjust size of positions to not exceed X% of portfolio or something like that. You can adjust the cash amount in portfolio to fluctuate from 0% to Y%.

- Run this 100K times

...

- Profit?

- Well, after you've run the 100K times, you should have a bell curve of returns and you possibly can do analysis of where in that bell curve your own IRR is...

Or is this not what you want to do? Or too complicated? Or other issues?

Edit: Hmm I wonder if anyone has done this for long term analysis of random returns. I.e. do this with a simple portfolio that starts with 10K on year XXXX and has no inflows/outflows (and/or adding \$Yk every year). Compare with investing in index? Seems like simple idea so I'd think someone would have done it...

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I am not very good in statistics, but it seems to me that what you described in first post is very different from what you described in the last one.

To deal with the last one:

- You know your own IRR and your cash inflow / outflow times and amounts.

- Build a model that buys/sells random stock to satisfy inflows/outflows. Also buy/sell at random other points within timeline (you can adjust trade frequency). You can also adjust size of positions to not exceed X% of portfolio or something like that. You can adjust the cash amount in portfolio to fluctuate from 0% to Y%.

- Run this 100K times

...

- Profit?

- Well, after you've run the 100K times, you should have a bell curve of returns and you possibly can do analysis of where in that bell curve your own IRR is...

Or is this not what you want to do? Or too complicated? Or other issues?

Edit: Hmm I wonder if anyone has done this for long term analysis of random returns. I.e. do this with a simple portfolio that starts with 10K on year XXXX and has no inflows/outflows (and/or adding \$Yk every year). Compare with investing in index? Seems like simple idea so I'd think someone would have done it...

Yeah, I think that's what I want but, honestly, that's probably too much work to justify.

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Hi All,

I'm trying to figure out a way to evaluate my portfolio's performance statistically, taking the idea that if you want to do something, you should probably measure it.

I have the problem of having switched from a portfolio of mutual funds to stocks over time as I've learned more. This creates a challenge evaluating my performance as the portfolio wide metrics are not appropriate (i.e. I'm fully aware that my mutual funding picking skill is shit).

So, I have records of each stock I've bought (when, how much, etc) and I've created a paper benchmark for each stock using a paper-traded portfolio of ETFs (i.e. if I bought 100 shares of AAPL on the Jan 1, 2016, I create a paper trade of VTI for the same dollar amount on the same day). This gives me a dollar-weighted benchmark for each stock, meaning that the IRR of each stock can be compared to the IRR of its benchmark. The difference between these two numbers can be thought of my "alpha" for the stock.

B/c's these "alphas" are independent(-ish) samples, I want to test them statistically. I think it's appropriate to weigh the alphas by age, (specifically, a "money weighted age" or, log base(1+IRR)[Gross Return] = age) The t-test isn't appropriate, but I think I sign-rank test is fine.

I'm not sure on the statistical test, but I'm not aware of a more appropriate model (quick Googling turned up nothing useful). If I do this, I get something reasonable, but any feedback/comments are appreciated

It's probably a lot easier to try to get some meaningful statistics by looking at the performance of your whole portfolio, not by looking at the IRR of individual stocks.

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• 2 months later...

I would suggest doing a portfolio approach, instead of analyzing each stock performance individually. First, the series are not going to be independent, so you are not losing much by not analyzing them separately. Second, only in this way you can capture diversification effects.

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