Adjusting Returns for Impact of Fees, Taxes, and Currency 77
are only realized upon the sale of a security, one way to defer taxes is to minimize turnover and hold securities within the portfolio for as long as possible. But because the investor will eventually withdraw his money, or liquidate the portfolio, there is a potential tax on the unrealized gains lurking in every taxable portfolio. Because of this tax overhang, investors also are interested in a measure of return that takes the potential taxes into account. We calculate such an after liquidation after-tax return by assuming that the investor sold all the securities in the account on the end date. To do this we calculate an assumed tax liability equal to the unreal- ized gain multiplied by the applicable tax rates, and then subtract the result from the numerator. Mutual funds must follow specific SEC direc- tions for calculating both before- and after-liquidation returns that are presented to investors in advertisements and other materials. Although the post-liquidation return is useful to the investor in identifying funds with large embedded unrealized capital gains, it is not always meaningful for the purpose of comparing investment managers. One reason is that the difference in time since the inception date of the portfolio, or vintage year, will influence the cost paid for the securities and therefore the unre- alized gain embedded in the funds being compared.
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EXHIBIT 6.4 Mutual Fund Balance Sheet
Mutual funds pool the investments of multiple individual participants and invest the proceeds in a portfolio of securities. Mutual funds and other commingled pools provide diversification and the benefits of professional investment management to investors. Shareholders receive a proportionate share of the capital gains and income earned on the fund’s holdings. Inves- tors buy shares of open-end funds directly from the investment company at the Net Asset Value (NAV) per share. The NAV per share is calculated each day by first calculating the gross assets of the fund, which is the sum of the market value of each of the securities and the cash holdings of the fund.
Thenet asset valueof the fund is then calculated by taking the gross assets and subtracting accrued liabilities to the fund including the fee payable to the management company and other expenses such as custody and transfer agency fees. Exhibit 6.4 illustrates the calculation of the fund’s NAV per share. At the end of each day, the net asset value per share is calculated by dividing the net asset value of the fund by the shares outstanding, including new shares purchased using new contributions into the fund that day. The new contributions are added to the equity capital of the fund.
(6.3) When an investor makes a contribution into a mutual fund, the fund company creates new shares with a value equal to the NAV at the end of the day the contribution was made. Mutual funds employ forward pricing, where the contribution is made at the NAV struck at the end of the day the contribution was made. This has a beneficial impact on the return mea- surement process in that the NAV per share does not have to be adjusted by cash flows in order to calculate a time weighted return. We can calcu- late a time weighted return on a mutual fund without knowing the total market value of the fund or the size and timing of cash flows. The cash
NAV per share Total assets Total liabilities– Shares outstanding ---
=
Adjusting Returns for Impact of Fees, Taxes, and Currency 79
flow impact has already been netted out of the return because additional shares are issued proportional to each contribution. For example, suppose we have a fund where a shareholder contribution is received on Day 1 for
$10. The shareholder receives shares equal to the contribution divided by the Day 1 NAV of $10, or one share. The money is made available to the fund manager the next day, and the additional share is included in the next day’s NAV calculation. Exhibit 6.5 demonstrates the calculation of the NAV per share and return when there are contributions into the portfolio.
If there were no dividend distributions to shareholders from the fund, we could calculate mutual fund returns with the ROI formula using the change in NAV per share. We do this by dividing the ending NAV per share by the beginning and transforming it into a return, as in Exhibit 6.6.
Mutual fund returns measured via the change in the fund’s NAV per share are inherently TWRs. When new contributions are made into the fund new shares are issued at the market value of the fund, and when withdrawals are made shares are retired. Because of this the NAV of the fund is equivalent to a wealth ratio relative to the original investment in the fund. The contributions and withdrawals do not affect the return calculated. But there is one complication: Because funds periodically pay out income and capital gains to the investor, we need to adjust for these distributions when we calculate a multiperiod return.
EXHIBIT 6.5 NAV Calculation with Contributions
EXHIBIT 6.6 Returns Calculated Using NAV Per Share
80 RETURN MEASUREMENT
Distributions
Capital gains and income earned by the fund are returned to the share- holder in the form of periodic dividend distributions. Income distribu- tions are made up of the income earned on the underlying investments in the portfolio, including dividend and interest accruals. Accrued expenses are deducted and then the net amount is distributed to the shareholder as a dividend. Each investor receives a total dividend equal to their shares outstanding on the ex-dividend date multiplied by the per share dividend amount. The ex-dividend date, or ex-date, is the date when new investors into the fund are no longer entitled to the recently declared dividend. The frequency of the distributions varies depending on the type of portfolio, but all mutual funds must distribute most of their gains to shareholders by the end of each year. The NAV of the portfolio will fall on the day the fund goes ex-dividend by the amount of the dividend (in addition to the market value change for that day).
Published mutual fund returns will be calculated assuming that the investor reinvests these distributions into new shares of the fund.