### Is expected return an arithmetic mean or geometric mean?

Posted:

**Fri Feb 29, 2008 9:01 pm**I wanted to confirm with you that the value that is input for the expected return in your simulator is an annual arithmetic expected return (versus the geometric or compound annual expected return). As an example, an annual return of 8% with a standard deviation of 15% would have an expected compound rate of return equal to 8% - 1.125% = 6.875%. The 1.125% is the square of standard deviation divided by 2. Is this correct? I made this assumption based on the following description from your documentation:

To demonstrate the importance of volatility on a retirement plan, try this experiment. Set the investing style to “Custom” and choose a value for “Return - Average” that you’ve used in other planners (for example 8%). Next, set the “Return - Std Dev” to zero and run the simulation. Note the results this produces then increase the “Return - Std Dev” by a few percent and rerun the simulation. Do this a few times with slight increases to standard deviation each time and notice how increased portfolio volatility (higher standard deviation) affects your plan. This exercise should demonstrate that risk matters. This is why a portfolio’s risk level or expected volatility must be taken into account in retirement planning.

I like your program. Is there a way to store my input values so that I don’t have to reenter them every time I visit the website?

Thanks,

To demonstrate the importance of volatility on a retirement plan, try this experiment. Set the investing style to “Custom” and choose a value for “Return - Average” that you’ve used in other planners (for example 8%). Next, set the “Return - Std Dev” to zero and run the simulation. Note the results this produces then increase the “Return - Std Dev” by a few percent and rerun the simulation. Do this a few times with slight increases to standard deviation each time and notice how increased portfolio volatility (higher standard deviation) affects your plan. This exercise should demonstrate that risk matters. This is why a portfolio’s risk level or expected volatility must be taken into account in retirement planning.

I like your program. Is there a way to store my input values so that I don’t have to reenter them every time I visit the website?

Thanks,