Using Adjusted Prices to Calculate Mutual Fund Total Returns
Summary
The document addresses why a mutual fund return calculated from raw closing prices and a separately added dividend may differ from the fund's published calendar year total return. The answer compares year-end adjusted closing prices for consecutive calendar years, explaining that the annual performance period starts from the prior year's close rather than the first trading day's price. The adjusted close already reflects distributions, so the example's adjusted prices produce a figure close to the reported performance.
It also raises the distinction between average annual return and annualized return. The answer suggests that average annual return may mean a simple average of each year's returns, but explicitly treats that interpretation as uncertain and asks for the source of the terminology if it does not fit. The exchange offers an illustrative reconciliation, not a comprehensive account of fund reporting conventions, reinvestment assumptions, or the compounding used in annualized returns.
Key ideas
- Calendar year returns use the previous year-end as the starting point.
- Adjusted closing prices incorporate distributions and can be used to estimate total return.
- The example's adjusted-price calculation closely matches the stated fund performance.
- Average annual return may refer to a simple average, while annualized return is a distinct measure.
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# Calculating returns for a mutual fund with dividends
# Calculating returns for a mutual fund with dividends
I'd like to calculate returns for a given mutual fund (in this case, PRWCX from troweprice). When I look at their published performance, it says the Calendar Year Total Returns for 2013 is 22.43% but when I try to calculate that using with a formula (end.price + dividend - start.price)/start.price I get something different.
The price on 12/31/13 is 25.66 (adjusted close is the same), there was a dividend of 1.54 on 12/13/13, the close price on 1/2/13 is 22.56 and the adjusted close is 21.25. If I calculate the return using the close price, I get 0.2056, and if I calculate based on adjusted close, it's 0.28. The fund has an expense ratio of 0.71% (as of 12/31/13) and even if I subtract 0.71% from my results, I don't get anywhere close to 22.43%. Does anyone know what I could be doing wrong?
Also, I'm wondering if someone could tell me how Average Annual Total Return (for say 5 years or 10 years) is calculated.
My goal is to compare returns of this mutual fund to returns based on the S&P500 or individual stocks.
## Answer by Shahar (score 1, accepted)
https://quant.stackexchange.com/a/14735
When we hear that the Dow is up for the day, it is not relative to the open, but rather to yesterday's close. Accordingly, I believe the yearly returns for 2013 are calculated, using the yearly adjusted closing prices, as $(C_{2013} - C_{2012}) / C_{2012}$.
I looked up adjusted closing prices on finance.yahoo.com: substituting $C_{2012} = 20.96$ and $C_{2013} = 25.66$ I get 22.42%, which is very close to their published performance.
Regarding your second question, average annual return (as opposed to annualized return) is probably calculated using a straightforward simple average of the annual returns of the last five or 10 years. If that does not seem to work, please refer us to where you have seen this terminology. Thanks!Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.