Splitting up investments (math help, please)

**disneysteve** · 01-01-2011, 03:38 PM

If MFA and MFB have exactly the same expenses and exactly the same return every day for 30 years, your end result will be the same.

When might there be a benefit? If there is a minimum account balance to avoid a service fee. For example, if the mutual fund company tacks on a $10 annual fee for each account under $10,000. Another example would be if there are different fund classes and at a certain account value, you get upgraded to the better class with a lower expense ratio (Vanguard does this with their Admiral shares).

**jIM_Ohio** · 01-01-2011, 06:18 PM

Originally posted by radionightster View Post

Ladies and Gentlemen,

A quick question. Is there a financial benefit found in not-splitting up investments?

For instance, lets assume Mutual Fund A (MFA) and Mutual Fund B (MFB) both have 8% returns. After 30 years, will I have more money if I only invest $10,000 in MFA, or will I do better if I invest $5,000 in MFA, and $5,000 in MFB, or will they be the same?

I guess this is really a question about how compounding interest works.

If anyone can walk me through the math, it would be greatly appreciate.

Happy New Years,
RN

lots of variables

8% is an average return...
if both funds have the same return every day for 30 years, with same expenses and same transactions, then both will have same amounts.

Focus on investment objectives- you would not want two funds with same objectives in same account. Diversify... buy one stocks fund and one bond fund, or one large cap stock fund and one small cap stock fund (for examples).

**snafu** · 01-02-2011, 11:09 PM

radion presents a complex question. There are some good books on asset allocation. Your library likely has R.A. Ferri's book 'All About Asset Allocation' which is really helpful for future planning, re-balancing your portfolio and adding diversification in a logical sequence without being influenced by media alarmists or sales reps.

**runj** · 01-14-2011, 12:49 AM

People also split to spread risk. For instance you can split the two amounts and invest in funds that have different portfolios. if one does badly the other will do well

**jpg7n16** · 01-14-2011, 08:15 AM

Originally posted by radionightster View Post

Ladies and Gentlemen,

A quick question. Is there a financial benefit found in not-splitting up investments?

For instance, lets assume Mutual Fund A (MFA) and Mutual Fund B (MFB) both have 8% returns. After 30 years, will I have more money if I only invest $10,000 in MFA, or will I do better if I invest $5,000 in MFA, and $5,000 in MFB, or will they be the same?

I guess this is really a question about how compounding interest works.

If anyone can walk me through the math, it would be greatly appreciate.

Happy New Years,
RN

How the math of compounding works:

Let's say you wanted to invest $10k. And that investment earns 8% in year one. The math is:

$x * (1+rate of return) = $new money after 1 year
$10,000 * (1 + .08) = 10,000*1.08 = $10,800

And the next few years, it does the same 8% again. Now you had 10,800 invested instead of 10,000
$10,800 * 1.08 = $11,664 *1.08 = 12,567.12 * 1.08 = 13,604.89 ....

And this just keeps going and going. But there's a way to simplify it. What's happening is you just keep multiplying by 1.08, so you can use an exponent:

$X * [(1 + rate of return)^(# of years)]

As an example, I'll do your original question from above. $10k @ 8% for 30 years:

$10,000 * [(1.08)^(30)] = $100,626.57

And splitting up the money won't change anything in a mathematical world - where the returns are known.

$5000 * (1.08^30) = 50,313.28
$5000 * (1.08^30) = 50,313.28
50,313.28 + 50,313.28 = 100,626.56 (different by 1 penny due to rounding)

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But in real life, you don't call up Vanguard and say "okay - how much will the stock market return this year?" and some nerdy math guy goes "well this year the market will return 7.86%." No one knows what the market will return before it happens. Math can easily explain what happened, but it cannot guarantee what will happen.

So like runj said, it is helpful to split up money to reduce risk - more specifically, to reduce variance.

Let's say the returns on the two funds mutual funds A and B (MFA and MFB) ran like so for the 1st 5 years:
MFA: 8%, 12%, -5%, 15%, 8%
MFB: 8%, -5%, 18%, -2%, 20.3%

Balance of $5k invested in each: (day 1 = 5k; balances shown at the end of each year)
MFA: 5,400; 6,048; 5,745.60; 6,607.44; 7,136.04
MFB: 5,400; 5,130; 6,053.40; 5,932.33; 7,136.04
Combined: 10,800; 11,178; 11,799; 12,539.77; 14,272.07

(To calculate the balances, just take the previous balance times 1 + the rate for that year. ex. $6,048*(1-.05)= $5745.60)

With $5,000 invested in each, you would end up with the exact same amount of money at the end of those 5 years, but wow what a ride to get you there! Some years, one fund was up a lot, while the other was down. But you'll notice that the combination of both securities had a balance that went steadily upward. Even though each fund had a few negative years, the total portfolio never had a negative year.

This is lowering the variance. The destination is the same, but the ride along the way isn't as bumpy.

Now that was easy to show cause I got to make the numbers whatever I wanted them to be. Usually, when fund A has a bad year, fund B will as well. But not always to the same degree. Maybe fund A lost 10%, but fund B only lost 5%. That still smoothes out the ride.

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Bonus section! You didn't ask for it, but here's how to calculate your average return over a period of years:

(Ending Balance / Beginning balance)^(1 / # of years) - 1 = average compounded return

So in my little example above:

(14,272.07/10,000)^(1/5)= 1.0737 - 1 = 7.37%
(7,136.04/5000)^(1/5)= 1.0737 - 1 = 7.37%

(100,626.57/10,000)^(1/30)= 1.08 - 1 = 8%

**bjl584** · 01-14-2011, 11:39 AM

Others have nailed this one pretty well. The math works the same. 8% is 8% whether split up or not. The results will always be the same. Focus more on diversification to spread out your risk.

Splitting up investments (math help, please)