Calculate investment percentages across two 401K accounts

Question

I would like to invest my 401K portfolio across the following fund categories:

• Bond Fund 5.0%
• Large Cap Fund 45.0%
• Mid Cap Fund 20.0%
• Small Cap Fund 15.0%
• Real Estate Fund 3.0%
• Foreign Fund 12.0%

The problem is that my money is spread across two employer-sponsored accounts. (I don't want to roll my old employer's account into my new.) Both accounts offer the above funds. However, in account 1, The bond, mid cap, and foreign funds have MUCH lower fees than their corresponding funds in account 2. So, I don't want to buy ANY shares in those 3 funds in account 2.

I need to calculate the % of each account that should be invested in each of the funds in order to achieve the above mix of funds in my portfolio overall. Note that 75% of my money is in account 1 and 25% is in account 2.

I would appreciate learning how to do this so that I can update the percentages as time goes on and more and more of my total invested money is in fund 2.

Answer 1

Call $B, L, M, S, R, F$ the desired percentage in each found, $b_1, l_1, m_1, s_1, r_1, f_1$ the distribution of investments in account 1 , $b_2, l_2, m_2, s_2, r_2, f_2$ the distribution of investments in account 2, $a=0.75$ the quantity of money in the first account.

We have $b_2= m_2= f_2=0$ as you don't want to invest in these founds from account 2.

You need $x_1*a+x_2*(1-a)=X$ (substitute $b, l, m, s, r, f$ for $x$ ).

So $b_1={B \over a}=0.07$, $m_1={M \over a}=0.27$, $f_1={F \over a}=0.16$.

The rest of the values need to be redistributed according to the remaining of the funds, we can do this using only the original percentages for the second account: $l_2={L \over L+S+R}=0.71$, $s_2={S \over L+S+R}=0.24$, $r_2={R \over L+S+R}=0.05$.

Now you can use again $x_1*a+x_2*(1-a)=X$ finding $l_1=0.36$, $s_1=0.12$, $r_1=0.02$.

Answer 2

The initial distribution does not need to be difficult. Add up the total amount in the two accounts combined; I don't need to know how much that is, so let's say the total is $P,$ with $0.75\times P$ in the old account and $0.25\times P$ in the new account.

If the accounts are administered in the usual way, you can make transactions in which you sell some amount of one fund and buy an equal amount of another. So you simply do this until the total amount in each fund is correct.

Since the bond, mid-cap, and foreign funds have the greatest constraints, it may make things easier to do them first. For example, if you have less than $0.05\times P$ already invested in the bond fund in the old account, transfer money from other funds in the old account into the bond fund until it has $0.05\times P$ invested. If you have more than $0.05\times P$ invested, transfer the excess into other funds.

You continue doing this with each fund in turn until every fund has the correct amount in it. Once a fund has the right amount, you stop making transactions in or out of it.

With regard to how much of each of the large-cap, small-cap, and real-estate funds is initially invested in the old account and how much is in the new account, you have indicated you do not have any constraints. Unless there are fees for the transactions, you do not need an "optimal" strategy for the sequence in which you transfer funds. As long as you do not touch any funds that already have the correct amount in them, you can continue making transfers from funds that have too much into funds that have too little, transfering as much as you can each time without bringing the "from" fund below its desired amount or making the "to" fund greater than its desired amount, and after a finite number of transfers you will be done.

By being cleverer, you might be able to slightly reduce the number of transactions you need in order to do the initial setup of the accounts, but the mental effort of working out the strategy may be greater than the effort of making the "extra" transactions.

The thing for which you may want a more sophisticated strategy is how you maintain the percentages as the funds grow and as you put additional money into the new account. Since you have ruled out the possibility of simply distributing each new deposit in the new account according to the desired percentage of the total amount (because that would mean making investments in the bond, mid-cap, and foreign funds in the new account), you will have to redistribute money in each account frequently. You could simply repeat the initial setup procedure every month, but in this case it seems worth setting up a more efficient method, since you will have to repeat it many times.

One possible strategy is this:

1. For each contribution to your new account, allocate $15\%$ to the small-cap fund, $3\%$ to the real-estate fund, and the remaining $72\%$ to the large-cap fund.
2. Periodically (each month, each quarter, or each time you make a contribution, depending on how much effort you want to put into this), transfer money from the large-cap fund to the bond, mid-cap, and foreign funds in order to bring each of them up to the desired percentage of the total amount in the two accounts.
3. Periodically (as often as you want, but probably less frequently than the previous steps; perhaps once or twice a year) make additional transfers between funds to restore them to the desired percentages of the total. This is necessary because in most years some funds will gain more than others.

A slight simplification of this strategy is to set fixed amounts for the transfers in Step 2 of this strategy. You may even be able to set this up to occur automatically at the same frequency as the contributions to the new account. If the amount of each contribution is $C,$ then for each new-account contribution you would transfer $0.05 \times C$ to the bond fund, $0.20 \times C$ to the mid-cap fund, and $0.12 \times C$ to the foreign fund in the old account. This accounts for the change in value of your accounts due to contributions. Step 3 would perform any additional adjustments to account for the differences in market gains between funds.

To make this work best, you will want to have plenty of money invested in the large-cap fund in your old account, since that is where the transfers in Step 2 must occur. The best initial distribution would therefore be to put as much as possible into the large-cap fund in the old account. This results in the following initial distribution: \begin{align} \text{Old account:}\quad & 0.05 \times P \text{ in the bond fund} \\ & 0.20 \times P \text{ in the mid-cap fund} \\ & 0.12 \times P \text{ in the foreign fund} \\ & 0.38 \times P \text{ in the large-cap fund} \\ \hline & 0.75 \times P \text{ total in this account} \\[6pt] \text{New account:}\quad & 0.07 \times P \text{ in the large-cap fund} \\ & 0.15 \times P \text{ in the small-cap fund} \\ & 0.03 \times P \text{ in the real-estate fund} \\ \hline & 0.25 \times P \text{ total in this account} \end{align}

To set this up, you transfer funds into or out of the bond, mid-cap, and foreign funds in the old account first, as before; then transfer all remaining money in the old account into the large-cap fund; then make any other necessary transfers within the new account.

Neither this strategy nor any other is likely to work forever. If you make enough contributions to the new account, it is likely that its value will eventually be much greater than the old account (even after market gains). Once the total in the new account is more than $1.703$ times the total in the old account, it will simply not be possible any more to maintain the desired investments in the bond, mid-cap, and foreign funds ($37\%$ of the total) without making some of those investments in the new account.

At that point, your only rational choice clearly is to get a new job with an employer whose 401(k) plan does not charge such high fees for those funds.