Calculating expected returns to funds

Summary: Funds come in two varieties: (i) unit trusts and (ii) investment linked products.  The latter are like unit trusts but sold primarily through Singapore’s 12 life insurance companies. 

There are 950 funds in Singapore, of which 400 are approved for investing your CPF ordinary account.

CPF data shows performance of the 400 CPF-approved funds over the past 3, 5 and 10 years. During this time, the majority of funds earned LESS than the 2.5 per cent paid by the CPF Board on members’ ordinary account. 

Sixty per cent have earned less than their benchmarks.  This statistic is compiled from data that uses a bid-bid basis of calculating returns to the 400 CPF-approved funds.   As such, it omits the initial commission of up to 5 per cent. It therefore overstates returns and understates the fraction of funds sold in Singapore which have failed to meet their benchmarks -- (the actual number failing to meet benchmarks would be higher than sixty per cent). 

Two arguments why CPF members are nevertheless better off to take money out of their CPF ordinary account and invest in funds are the following:

First, in boom periods, funds will earn more than CPF.  And in all periods, the average performance of funds will exceed CPF's 2.5 per cent.

Second, even if the average return of funds is below CPF’s 2.5 per cent, some funds earn more.  Invest in those. Use the expertise of banks, life insurance companies and financial planners as they can predict which will be the top-performing funds in the future.

This study shows that the first argument is incorrect.  After all costs are considered, stock funds earn only slightly more than the 2.5 per cent paid by the CPF ordinary account. The small premium, however, is not enough to justify the added risks.

The second argument is also incorrect.  There is a substantial literature which tests whether past fund performance is a good predictor of future performance.  The literature is based on US data and shows that it is not.

I have also done a study of Singapore funds which also found no persistence in returns between two 3-year periods.  The top performing funds in the early period were equally likely to be top or bottom performers in the subsequent period.

Bottom line: This study looked at returns to funds vs. CPF ordinary account.  It made conservative assumptions: (i) that returns were at the high end of estimates and (ii) costs were at the low end. 

The result is that funds are estimated to out-perform the CPF ordinary account's return -- but not by much.  The expected return to funds (after all costs) is 4.8 per cent vs. 2.5 per cent for CPF ordinary account. 

This 2.3 per cent difference is a small risk premium and unlikely to justify the much higher risk of funds vs. CPF's risk-free returns.

Calculations:

Explanations of Revenue and Cost items:

1) Total Returns.  It shows the total expected return to funds.  This is also the gross returns. 

The return since 1985 to the STI (Straits Times Index) is 7 per cent.  The return since 1985 to the MSCI (Morgan Stanley Capital International) – a global stock index -- is 11 per cent.  The return since 1926 to the US markets is 12 per cent.  (This data is from Roger Ibbotson, “Stocks, Bonds, Bills and Inflation”.)  The return since 1800 to US markets is 10 per cent.  (Data is from Jeremy Siegel from the Wharton School at the University of Pennsylvania.)

The US data may be the most appropriate because it is more robust: It covers a very long time series and includes more shares.  (Except for the very early years, it includes the 500 shares of the S&P 500 stock index.)

It would seem that Singapore stock data would be most appropriate. Unfortunately, the time series is too short.  The 7 per cent return to the STI since 1985 most likely understates the true expected return for Singapore shares.

Using a Singapore index is also not appropriate because the proportion of Singapore shares included in the 425 CPF-approved index funds is very small.  Nearly all of the 425 CPF-approved funds are foreign funds which invest in foreign shares.

Also, calculations were made assuming a 12 per cent return because it is at the high end of return estimates. This gives a conservative bias – (i.e. the performance of funds relative to CPF is probably even worse than shown here).

2)  Expense ratio.  The expense ratio for funds in Singapore is estimated at 2.0 per cent.  (See calculations here.)

3 a)  Taxes deducted at source including tax inefficiency is estimated at 0.8 per cent. (It is likely on the low side.)

(i) Taxes: These are paid and deducted at source. It varies from country to country. It includes taxes on dividends and interest income.  Often, the taxes are grouped under "withholding".  The withholding rate for non-US persons is 30 per cent in the US.  It applies to dividends and most interest income. It is a hidden expense and not reported in the expense ratio. It is estimated at 0.8 per cent. 

(ii) Tax inefficiency: The taxes paid by Fidelity Funds, the largest family of funds in the world was 3 per cent per year over the period from 1986 to 2000.  Like the 400 CPF-approved funds, Fidelity funds are almost entirely managed funds (and not index funds).  

The second largest fund in the world, Vanguard Group of funds, paid taxes of 1.4 per cent during the period from 1986 to 2000. The difference between taxes paid by Fidelity’s actively managed funds (3.0 %) and Vanguard’s mostly passively managed funds (1.4 %) equals 1.6 %.  This is the tax inefficiency.

[Footnote: Foreign funds will not pay capital gains taxes on share purchases. But they will pay indirectly if they own US funds, as they are subject to capital gain taxes.  To be on the conservative side, none of the 1.6 per cent cost of tax inefficiency was included in the estimate of hidden costs.]

3 b)  Broker costs including soft-dollar rebates.  The broker costs are commissions.  Because of higher turnover, managed funds incur more brokerage commissions than passive funds.  

Adding to the commission cost is the kickback system.  It is rampant in the industry.

It is politely called “soft dollar rebates” or “soft money rebates”.  It involves brokers making payments in the form of gifts to the fund.  Popular gifts are subscription to a Bloomberg news terminal, software, stock market analysis including newsletters and similar items the fund may request. 

In return, the fund pays the broker a higher commission on trades. Typically, the fund will pay the full broker-assisted commission with no discounts.

Most funds engage in soft dollar rebates and the funds mention this practice in their prospectus and sometimes in annual reports.  It is usually not mentioned in fact sheets. Most funds are careful to point out that the rebates do not include trips or vacations for staff.  No funds tell the amount of the rebates. 

It is not clear why the interests of fund holders are better served by funds paying high commissions to brokers and getting part of it kicked back to them in the form of business gifts vs. a more business-like procedure where funds negotiate for the lowest commissions.  With their large trading volume, funds could negotiate for the lowest rates.  (The funds could then use the savings to buy their own gifts, if needed.)

3 c)  Forex Costs. Based on the bid-asked spreads, these are estimated at 0.25 per cent one way and 0.5 per cent round trip (to buy and sell).

It is the foreign exchange costs of converting from the home currency (Singapore dollars) to a foreign currency.  This is necessary for all foreign fund purchases.  Of course, it makes no difference if the investor purchases the foreign stock fund in Singapore dollars. The fund still needs to convert from Singapore dollars to purchase the foreign fund.  

As with all hidden expenses, the cost of the conversion is deducted from the yield.  In the terminology of the fund industry, “this cost is transparent to the investor”. (It means the cost is “hidden from” the investor.)

3 d)  Currency fluctuations. This cost is estimated at 0.5 per cent. It arises when the fund invests in foreign shares.  This results in a second risk to the fund.  The first risk is that of share price fluctuation.  The second risk is from currency fluctuation.

3 e)  Long-term rise in the Singapore dollar.  It is estimated at 0.3 per cent per year.

Of course, fund investors will hold foreign and not Singapore denominated assets during the period they are invested in a foreign fund. (As mentioned before, nearly all of the 425 CPF-approved funds are foreign funds.)

You can think of this cost as an opportunity cost of not being invested in the Singapore dollar when it appreciates (goes up in value).

Will it appreciate?  Economic theory shows that in the long-run, the relative value of currencies is determined mainly by differences in productivity rates between countries.

Singapore’s high productivity has resulted in the gradual appreciation of the Singapore dollar against most currencies over the past 40 years. In recent years, this appreciation has halted, but it is expected to continue as Singapore’s productivity is expected to remain high.

3 f)  Cash drag.  It is estimated at 0.2 per cent.  This cost results from the need of funds to hold cash for redemptions.  (This is true for both index and managed funds.)

Managed funds also hold cash between their purchases of shares and as part of a market timing trading strategy.

4)   Amortized initial commission.  This is estimated to cost 0.6 per cent.  It is assumed the initial commission is 3.0 per cent and the average holding period is 5 years.  ((3.0/5) = 0.6 per cent.)

5)   Survivor and Incubator Bias.  This is estimated at 1.5 per cent.  It is not a cost, but a bias in the data which causes reported fund returns to be too high.  As a result, the expected return to funds is overstated. 

Survivor bias is estimated at 1.2 per cent. It results from measuring the returns of only the funds which survive vs. measuring returns of all funds. The funds which fail are those with very low returns -- but those low returns are not considered in calculating average fund returns.  Why?  Because the funds are dropped from the sample when they go out of business.  This makes fund returns look better than they really are.

A study of survivor bias by Princeton's Burton G. Malkiel and University of Southern California's Mark Carhart place survivor bias from 1.5% to 3.1% per year. I have used an estimate below the lower end of the estimate: 1.2 per cent.

Their study looked at 355 funds in 1970.  By September 30, 2001, only 158 (44.5 per cent) of these funds were still in business.  The majority had gone out of existence.

Incubator bias is another distortion and is estimated to cost 0.3 per cent.  It happens when a large fund group does not open the fund to the public until it reaches a critical mass. The fund is initially open only to a limited number of institutional investors. 

When it reaches that critical mass, it has either developed a good track record or a poor one.  The parent fund, drops the poor performing funds and brings the high performers to the retail market. Of course, this gives an upward bias to fund performance statistics.

In the US, a recent ruling by the Securities and Exchange Commission permits fund families (which may have more than 100 funds under management) to drop unsuccessful incubator funds from its performance data.

10) Risk Premium to Funds (not shown in the table).  It is estimated at 9 per cent.  The estimate comes from taking the expected market return of 12 per cent and subtracting the long-term risk-free rate.  This is assumed to be the treasury bill rate.

Data comes from Ibbotson, “Stocks, Bonds, Bills and Inflation”.  It shows that over the period 1926 to 2003, the return to stocks is 12 per cent and the return to treasury bills is 3 per cent.  

11) Risk-adjusted return to Funds.  It is the difference between the expected return to Singapore funds (12 per cent) and the risk-free rate (3 per cent – see 10).  It is 12.0 – 2.5 =  9.5 per cent.

The intuition is that investors should expect to receive 9.5 per cent over the risk-free rate of return as compensation for taking on the added risk of stock funds. 

The problem is they do not receive 9.5 per cent.  Their risk premium is only 2.3 per cent (4.8 - 2.5).

Two other costs, not included in the above:

a)  There are two costs charged by local banks for administering a CPF investment account: (i) $2 per 1,000 shares/units or part thereof per transaction.  Max charge: $20.  (ii) $2 per counter or per unit trust each quarter (each 3 months). 

Of course, item (i) gives investors an incentive to avoid low priced shares to minimize the charge of $2 per 1,000 shares.  The maximum charge per transaction would be for 10,000 shares x $2 = $20.  Item (ii) gives the investor an incentive to purchase just one counter or one unit trust.  It discourages purchasing many counters and this limits diversification.  It is not clear what are the benefits to the bank, society or the investor from these two incentives.

b) Cost of direct fund purchase by feeder, not from mother fund.  A feeder fund may get most of its investments from the mother fund.  But it may occasionally purchase other funds, itself.  The expense ratio of these other funds may not be included in the feeder fund's expense ratio. Recently, some funds which do this have started showing two expense ratios -- with and without this cost.

Conclusion:  Two factors keep investors from realizing the full potential of funds: Costs and an upward bias in the fund data.  Of these, the larger component is costs. 

Fund costs can also be divided into two categories.  The first is stated expenses such as the initial commission and expense ratio. The second are the 6 types of hidden expenses (a - f in the table).

Of the two, the larger component is hidden expenses.  

Funds are successful at piling fees into hidden expenses partly because investors never see them.  As a result, funds are perceived as being better bargains than they really are.

Hidden expenses remain unseen because these costs are deducted directly from the NAV (Net Asset Value) of the fund -- (from the fund's yield).  The investor probably does not suspect hidden costs are holding down his fund’s value. 

The investor is likely to attribute it to poor market conditions or poor earnings of the stocks in the fund’s portfolio.

Poor market conditions and poor company earnings are a temporary problem.  A fund will resume its growth path when conditions improve. 

Expenses, however, are a permanent problem. A fund whose growth is held down by expenses cannot expect to eventually meet or exceed its benchmark return.