CAGR, SD, DD

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caymann
Posts: 7
Joined: Sun Mar 20, 2016 4:10 pm

CAGR, SD, DD

Post by caymann »

I want to simulate a portfolio with
CAGR = x%
Standard Deviation = y %
Maximum Drawdown = z %

How should i do it?
jim
jimr
Posts: 821
Joined: Thu Feb 28, 2008 6:48 pm

Re: CAGR, SD, DD

Post by jimr »

First, the simulation doesn't support a maximum draw down percent parameter, so that would be tough to model.

The planner takes an average annual return for an input, not a geometric mean or CAGR. Generally, the CAGR associated with a given mean annual return will be a few dozen basis points lower and is dependent on the standard deviation. The higher the SD, the greater the difference between the average return and the CAGR. As an example, with the planner's moderate risk portfolio, the average return is 8.0% and the SD is 9.9%. Running a simulation with all the default parameters and a portfolio value of $500,000 produces a geometric mean or CAGR around 7.5 or 7.6%. If you set the portfolio type to custom and use the same 8% mean return but use 4% for the SD, the resulting CAGR is around 7.9%.

One way to convert between CAGR and average return is to use trial and error. After running the planner with a given set of inputs, click on the "Show all runs" button on the main planner window to pop up a window that shows a summary of each run. This summary includes the average return and standard deviation inputs along with the average geometric mean that resulted from those inputs.

By trial and error, you could try adjusting the average return input and running the planner until the CAGR output matches the desired value.
caymann
Posts: 7
Joined: Sun Mar 20, 2016 4:10 pm

Re: CAGR, SD, DD

Post by caymann »

I played with GM and AM and see what you mean.
I assume the definition of SD for both GM and AM remain the same so i can keep the SD the same for both cases, right?

As far as DD is concerned, i was wondering if that could be built into the SD
So for example S&P500 had a near 50% DD in 2008 but the SD is 20.2% in the calculator
Could i say, that 1xSigma=20% (ie 68% of the results), 2xSigma = 40%(95% of the results) and 3xSigma =60% (actually 50% to match the DD)(99% of the results) ?
The way i calculate 2xSigma = 20% from 1xSigma and then add 20% to get 40%
Similarly i calculate 3xSigma = 40% from 2xSigma and then add 20% to get 60%

I am doing this to catch those outliars (which do happen when market takes deep dive) into the simulation
essentially covering 3xSigma (or 99% of coverage) and addressing deep DD in the market

Does this make sense or am i thinking this wrong?
jim
jimr
Posts: 821
Joined: Thu Feb 28, 2008 6:48 pm

Re: CAGR, SD, DD

Post by jimr »

caymann wrote:I assume the definition of SD for both GM and AM remain the same so i can keep the SD the same for both cases, right?
That sounds right. SD is connected to the series of discrete annual returns that are used to compute a given AM or GM.
As far as DD is concerned, i was wondering if that could be built into the SD
So for example S&P500 had a near 50% DD in 2008 but the SD is 20.2% in the calculator
Could i say, that 1xSigma=20% (ie 68% of the results), 2xSigma = 40%(95% of the results) and 3xSigma =60% (actually 50% to match the DD)(99% of the results) ?
The way i calculate 2xSigma = 20% from 1xSigma and then add 20% to get 40%
Similarly i calculate 3xSigma = 40% from 2xSigma and then add 20% to get 60%

I am doing this to catch those outliars (which do happen when market takes deep dive) into the simulation
essentially covering 3xSigma (or 99% of coverage) and addressing deep DD in the market

Does this make sense or am i thinking this wrong?
I think that works, but I wonder if it'd be simpler to explore the impact of a market crash by just forcing it to happen explicitly in the simulation. To do this, use additional inputs and put in single year return/std entry with the return set to the size of the correction (say -50%) and the std dev set to 0. You could even experiment with different timing for the crash to see the impact (eg right after retirement, mid retirement, toward the end of the plan).
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