Should you prefer a mutual fund to have a high share price or low share price?
Mutual funds publish their per-share price on every trading day. Some of the share prices are in the single digits, some are in their teens, and some are even at (or close to) the century mark. Do these fund prices tell us which fund is cheaper? Or which fund is more “value-for-money”? Or which fund should we buy?
Theoretically, the answer is that the fund price by itself does not give any information to any of the questions posed. And there should not be since the share price is simply the result of dividing the total assets of the mutual fund by the number of shares allocated.
Let’s illustrate with a simple example.
Suppose a mutual fund has 50 million dollars in assets. If it is allocated into one million shares, then each share would be worth $50. On the other hand if it is divided into 10 million shares, then each share would be worth only $5.
However, having said that, in the world of finite decimal precision, there are differences between a fund with a high price and one with a low price. This has to do with the way the number of shares is calculated when an investor makes (or redeems) an investment.
When an investor purchases a fund, there are two main sources of rounding error when the number of shares is allocated to the investor.
- Share price : share prices are quoted up to the penny (step size = $0.01). For example, for a fund with a declared share price of $5.00, the “true” NAV could be anywhere between $4.995 to $5.005. In the worst case, the rounding error is half of the step size, i.e. $0.005 or about 0.1% for a share price of $5. For a fund with a share price of $100, the worst case rounding error is much less, at 0.005% (half of $0.01/$100).
- Share quantity : the number of shares allocated to each investor is rounded to three decimal places. This step size is 0.1% per unit share, i.e. the worst case error due to share quantity rounding is 0.05%. For a fund with a share price of $5, the worst case error would be 0.05% x $5 = $0.0025; for a fund with a share price of $100, this error would be 0.05% x $100 = $0.05.
It is not difficult to calculate the overall worst case rounding error for funds of different prices and with different fund purchase (or redemption) amounts. This is shown in the table below.
The table shows that for a fund priced at $5, the worst case rounding error for a one-time investment amount of $1000 is $1.003. If the investment is $10,000, the worst case rounding error is $10.003.
On the other hand, if the fund is priced at $100, then the worst case rounding error for a one-time investment amount of $1000 is $0.10. If the investment is $10,000, the worst case rounding error is $0.55.
It is interesting to see how an improvement in one decimal-place precision (to four decimal places) in the calculation of the share quantity allocated will reduce the rounding error. The table below illustrates this. Interestingly the rounding error does not reduce significantly. Having a higher share price is actually still more important.
In conclusion, all other things being equal, a fund with a higher price helps to reduce the rounding error when the number of shares to be allocated is calculated. For this reason, a mutual fund share split simply does not make sense in my opinion.
Stumble it!
