Mutual Fund Investment vs GIC

[apostruk]

This may be of interest to those of you who have mutual funds.

I used the monthly gains or losses of my mutual fund to model how this investment would compare with a GIC. The idea was that on any given month, I can compare the interest rate of my mutual fund (as a function of annual compound interest) to the current GIC rates calculated on a per-annum basis.

To do this, I used the standard Compound Interest Formula, with interest applied 1/12 times (n) per monthly time period (t). My original investment is (P), and (A) is the amount following each month. My math to capture this function is shown in the attached image.

Unlike a GST investment that has a constant interest rate, the gains and losses in mutual funds can fluctuate daily. However, I only receive data once a month.

A six-year plot of interest rate (r) vs monthly payment period (t) shows large oscillations at the very beginning that quickly settle down. (see attached plot). I've also included a trend line for what it's worth.

Please let me know if my model is reasonable or if it is even correct, and if there may be a better way to do this.

Thank you.

 

[JeffM]

I do not know how you did the curve fitting, but it looks from casual inspection as though the curve is a mathematically good fit.

But it seems to me that creating a smooth curve that looks as though volatility is tiny obscures the crucial fact that volatility is material. Your mathematics may be technically correct but applied inappositely. Part of this is that the idea of comparing an investment that is designed to allow for big gains at the expense of high volatility and an investment that is designed to provide stability at the expense of a limiting returns to a modest level is like comparing a steak knife to a soup spoon: they are tools for a different purpose. You will starve trying to eat soup with a steak knife and will also starve trying to eat steak with a soup spoon.

You might get more informative results by comparing your mutual fund to a broad-based stock index. Both will show considerable volatility; both should show generally similar returns. You can then ask whether your mutual fund gives a higher return but higher volatility (perhaps attractive to you), a lower return with higher volatility (certainly unattractive to anyone), a lower return but also lower volatility (perhaps attractive to you), or a higher return with lower volatility (certainly attractive to anyone).

To be helpful, mathematics must be technically correct and also be applied in a way that makes sense.

PS Comparisons should be made over periods that are relevant to you. If you are a day trader, you should be averaging over days. If you are in your sixties planning for retirement, you should be averaging over longer periods, a year at least.