## Portfolio average rate of return & standard deviation

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Topic Author
Cincy_1988
Posts: 15
Joined: Tue Jun 04, 2024 10:21 pm
Location: Ohio

### Portfolio average rate of return & standard deviation

Hello

My retirement portfolio consists of a large of mutual funds for which I've limited historical (1 year, 3 years, 5 years, 10 years, since inception) rates of return. Frankly, I couldn't understand how to use Simba's spreadsheet (mostly because it doesn't have the data for my mutual funds - at least I couldn't figure out how to add to the spreadsheet). So, this is what I did:

1) Using the historical rates of return, I calculated the average & standard deviation of each fund.

2) Using the average & standard deviation from step 1, I conducted Monte Carlo Simulation (with 1000 cases) for each fund assuming a normal distribution.

3) Using the Monte Carlo Simulation data, I calculated my portfolio rate of return as (w1*x1+w2*x2+w3*x3) where w1 w2 w3 = weight of each fund and x1 x2 x3 = average rate of return of each fund.

4) Using the Monte Carlo Simulation data, I calculated my portfolio standard deviation as: SQUARE ROOT OF (w1^2*s1^2+w1*w2*s12+w1*w3*s13+w1*w2*s12+w2^2*s2^2+w2*w3*s23+w1*w3*s13+w2*w3*s23+w3^2*s3^2) where w1 w2 w3 = weight of each fund, s1 s2 s3 = standard deviation of each fund, and s12 s13 s23 = covariance between funds 1&2 1&3 2&3 (I used Excel's COVARIANCE.S function).

I've put my Excel file on the following OneDrive:

https://mailuc-my.sharepoint.com/:x:/g/ ... w?e=X0Z4hb

I'm a structural engineering professor and investment isn't my field!! I appreciate if somebody can let me know if my approach makes sense.

Thanks,
Bahram

p.s.
I would like to thank Prof. Moy from St. John’s University for sharing his paper regarding portfolio standard deviation.
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### Re: Portfolio average rate of return & standard deviation

Welcome! Sorry, but you don't need any of that to understand investing.

See the wiki: Getting started

May I suggest you post your portfolio information in this thread using the Asking Portfolio Questions format? It will make you think about the "big picture" while giving us the information we need to point you in the right direction.

If you have any questions, ask them here.
To some, the glass is half full. To others, the glass is half empty. To an engineer, it's twice the size it needs to be.
Thesaints
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### Re: Portfolio average rate of return & standard deviation

You can't estimate future return with any useful accuracy by using historical data only, however you process it.
retired@50
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### Re: Portfolio average rate of return & standard deviation

Cincy_1988 wrote: Sun Jun 09, 2024 2:10 pm
I'm a structural engineering professor and investment isn't my field!! I appreciate if somebody can let me know if my approach makes sense.
Welcome to the forum.

You're overthinking it. The future is unknown. Stop wasting your time trying to estimate future returns.

Successful investing is about behavior, and avoiding bad behavior(s). It's not like choosing the incline angle of a staircase, or the pitch of a roof.

We invest in the stock market because we believe in capitalism, global economic growth, or whatever you want to call it. Historically, that has worked out well. So we arrive at the conclusion that, according to what we think is statistically likely, you'll be better off in 25 years. Is it possible that the market will dip between now and then, of course, but it may not matter (much, or at all) over the long haul.

Regards,
"All of us would be better investors if we just made fewer decisions." - Daniel Kahneman
afan
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Joined: Sun Jul 25, 2010 4:01 pm

### Re: Portfolio average rate of return & standard deviation

Welcome to the forum!
the answers to your questions depend on why you are doing this.
I can see two alternatives:
1. "I am new to investing but, as an engineering professor, not at all afraid of math. I would like to have some fun inspecting data and running models. This will have essentially no effect on my investing or personal finance behavior".
2. "I am new to investing and want to optimize my approach to my personal investments."

If "1", then I would start by reading an introductory finance textbook. I would probably use Bodie and Kane, but there are others. If your university has such a course, you could ask the instructor for suggestions, particularly for someone who is comfortable with math at a higher level than the undergrad prerequisite for the course.
This will provide you with some important background for why what you have done so far will not work.
Among other things, the returns to the stock market are not normally distributed. Assuming Gaussian for a MC will ensure that your results are nonsense. Also, the returns to your funds are almost definitely not independent. If you want to model their standard deviation, you will need a variance/covariance matrix as an input.
Finally, unlike structural engineering where, I hope, the inputs are reasonably well predicted, there is a large unknown variance in market returns. The unknown component is so large that efforts to predict returns are doomed. Once you get into it, you can start reading the extensive literature on predicting performance and you will quickly see that all the tools and data in the world generate predictions that are, at best, barely better than simply assuming long term averages.

If you have the historical data for your own portfolio, then you can calculate what the SD has been directly from that, with no need for MC or any other simulations. If you want to do "what if" models to see what the effects of different asset allocations would have been in the past, you can use a tool like portfolio optimizer, which will let you change allocations and report the realized means and SD.
If you want to predict what future returns might be for a given set of allocations, then dive into the investment text, then do the work for a graduate-level course, and develop models more like what your finance professors would use. But recognize that the results are no more than educated wild guesses.

On the other hand, it IS fun to play with the data.

2. If your goal is to optimize your investing, then you need almost none of the above. I would still read an introductory investment text because it will explain the reasons underlying a rational approach, but you would have no need to try to model anything.
We don't know how to beat the market on a risk-adjusted basis, and we don't know anyone that does know either | --Swedroe | We assume that markets are efficient, that prices are right | --Fama
Topic Author
Cincy_1988
Posts: 15
Joined: Tue Jun 04, 2024 10:21 pm
Location: Ohio

### Re: Portfolio average rate of return & standard deviation

Thank you all for your detailed replies. You folks are right; I can't predict the future.
Chuckles960
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### Re: Portfolio average rate of return & standard deviation

In the systems studied by physical sciences and engineering, one can (or one can hope to, by diligent research) predict the future. In the rest of the world, not so much.

But the OP is not the only one to think that math can be used to extrapolate into the future. There's way too much of that in the investing world. For example, Fidelity runs (or pretends to run) a million simulations and confidently predicts that I will have enough to live on in retirement as long as I spend no more than \$x. Yeah, right.

Even on BH, where many people are very smart and able to cut to the chase (see previous posts), there is way too much formulaic thinking, e.g. "If you have x times current annual expenses you have won the game and can stop playing".
Topic Author
Cincy_1988
Posts: 15
Joined: Tue Jun 04, 2024 10:21 pm
Location: Ohio

### Re: Portfolio average rate of return & standard deviation

I agree! In structural engineering, we use historical data and simulations to develop design loads (snow, wind, tornado, earthquake, etc.) but we use load factors (to increase the loads) and reduction factors to reduce the strengths to make sure structures have a small probability of failure (typically 1 in 10,000). There's no certainty in any field, especially in finance/investment.

Thank you for reminding me about the real life!
afan
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Joined: Sun Jul 25, 2010 4:01 pm

### Re: Portfolio average rate of return & standard deviation

Another difference is that, to a large extent, you think you know how your systems work. You can use the same factors to compute stresses today and expect that they will predict stresses tomorrow. For investments, people have a very good idea of the short-term relationship between interest rates and bond prices. However, the correlation between international stock returns and domestic returns, for example, bounces around widely and no one thinks there is a reliable answer to how they are related. Same for just about any other determinant of stock prices.

It can be quite entertaining. Every year major investment companies publish their predictions of market returns. I have never seen one review their past predictions and compare them to the outcomes. I assume they know, but that their predictions are so poor that they do not want to bring it up.
We don't know how to beat the market on a risk-adjusted basis, and we don't know anyone that does know either | --Swedroe | We assume that markets are efficient, that prices are right | --Fama