What is Standard Deviation for investment returns?

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mountainsoft
Posts: 37
Joined: Sun Jan 22, 2017 8:34 pm

What is Standard Deviation for investment returns?

Post by mountainsoft »

I apologize for the ignorance, but what exactly is "standard deviation" for the investment returns? I tried to Google it, but the math and equations mean nothing to me. :)

I'm guessing the Average Return is kind of the "middle point", and the SD is how much the return can increase or decrease around that point?

I figured out I could enter a fixed Average Return and leave the deviation set to zero. That works as a sort of worst case scenario, if I enter the worst return my IRA has had in the past.

However, I'm interested in experimenting with different returns. Vanguard says my IRA investment (VBIAX) says it has a standard deviation of 6.5%, but I'm not sure what value to use as the Average Return? Should that be the 1 year, 5 year, 10 year, or since inception returns?

Thanks,

Anthony
jimr
Posts: 821
Joined: Thu Feb 28, 2008 6:48 pm

Re: What is Standard Deviation for investment returns?

Post by jimr »

Most Monte Carlo retirement simulation models are built on the underlying assumption that over time investment returns roughly follow a normal distribution. This assumption is probably not entirely accurate, but modeling returns using the normal distribution is close enough to the real world to generate useful results and most importantly, it's a reasonable way to account for the volatility of portfolio returns, especially compared to just ignoring volatility and assuming your portfolio gets the exact same average return each year.

The key to building a good retirement plan is to take into account the reality that investment returns are not steady from year to year. This unsteadiness, or volatility of returns, introduces a special kind of risk into a retirement plan called sequence of returns risk. It turns out that even if your portfolio enjoys a decent average return over your retirement, the exact sequence of returns that your portfolio experiences can have a big influence on the success of your plan.

So without getting too deep into the statistics, standard deviation is one of the two parameters that are needed to characterize something that follows the normal distribution. Average is the other parameter (in investing, average return). Standard deviation characterizes the year to year variation around the average that a sequence of returns is likely to follow.

This is a big topic and it's tough to do it justice in a short post, but hopefully with that background you'll have better luck with google. For starters, I'd suggest looking at google results pointing to wikipedia entries on this subject. Wikipedia entries can have problems sometimes, but generally it usually does well with topics like this.
JoelAlbert
Posts: 7
Joined: Tue Jan 10, 2017 12:21 pm

Re: What is Standard Deviation for investment returns?

Post by JoelAlbert »

Jim,

Just to check my understanding as well...

If I enter 4% as the Average and 6% as the std Dev, the Monte Carlo will be simulating returns in a range of -2% to 10% assuming a normal distribution of outcomes.

Is that close to right?

Joel
mountainsoft
Posts: 37
Joined: Sun Jan 22, 2017 8:34 pm

Re: What is Standard Deviation for investment returns?

Post by mountainsoft »

jimr wrote:it's a reasonable way to account for the volatility of portfolio returns, especially compared to just ignoring volatility and assuming your portfolio gets the exact same average return each year.
Is there any real advantage to using an average and deviation for the returns, instead of just picking a fixed return based on the funds lowest performance?

I'm not really interested in how GOOD the portfolio might do, I mostly just want to know if it will last in the long term in the worst case. For example, if the fund dives and stays at it's lowest level my entire retirement. :)

Thanks,

Anthony
jimr
Posts: 821
Joined: Thu Feb 28, 2008 6:48 pm

Re: What is Standard Deviation for investment returns?

Post by jimr »

That's very close but not quite 100% right. The returns that the simulation generates will fall within that range around 68% of the time. That's because of the characteristics of the normal distribution and the definition of standard distribution.

Taking this further, returns will be between -8% and 16% around 95% of the time (this is 2 standard deviations). This is again based on how standard deviation works with the normal distribution. The shape of the normal distribution is such that about 95% of the variation around the mean is covered by two standard deviations.

To make this more concrete, consider that each run of the planner does 10,000 simulation iterations or paths through your retirement and each requires maybe 30 random portfolio returns to get generated (if your plan is 30 years long). That means each time you run the planner, the simulation will generate 300,000 random portfolio returns. With your 4% average return and 6% std dev example, around 15,000 of the 300,000 portfolio return values would be outside of the range of -8% and 16%. OTOH, around 285,000 of the returns generated would be between -8% and 16% and around 204,000 of the 300,000 returns would be between -2% and 10%.
jimr
Posts: 821
Joined: Thu Feb 28, 2008 6:48 pm

Re: What is Standard Deviation for investment returns?

Post by jimr »

mountainsoft wrote:Is there any real advantage to using an average and deviation for the returns, instead of just picking a fixed return based on the funds lowest performance?
The advantage of using a tool that accounts for volatility is that imo it should produce a more accurate representation of reality.

Even using a very pessimistic but fixed value for return will likely understate the worst case scenario. Again, this is because this approach doesn't take into account the chance of getting a very bad sequence of returns.

The reason that the planner does 10,000 simulation iterations each time you hit run is to be sure to gather enough data that several cases where you had very bad luck (eg a very bad sequence of returns) are included in the analysis.

This is also why most financial planners tend to advise clients that a plan with a 90 or 95% probability of success is probably good enough. Because the planner works so hard to find all the cases of very bad luck, it's very difficult even for a very robust retirement plan to show a 100% chance of success.
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