# How to calculate annual returns from daily prices?

Suppose I have daily adjusted closing prices for SPY, for example from yahoo finance. How from this calculate annual return?

Note: It's NOT about issues like 1.2 means 20% or 0.2 means 20%.

The most trivial solution is:

(adj. closing price at 31.12)/(adj. closing price at 1.1)


But:

1. Result is different from the data appears on the web.
2. The data appears on the web is not adequate. For example from here 2014 return was 11.39%, but from here it's 13.46% (This first result on Google so I suppose it's reasonable resource). Same one can find clicking other web sites...

Thanks,

• If you have daily prices, then why not just throw away all the middle ones and take the return as final/initial? – will Dec 1 '16 at 13:47

My formula example does not include cash dividend, management fees (ie. SPY), holding taxes.

Daily %=(px[i]-px[i-1])/px[i-1], where px[i] today and px[i-1] is yesterday.

Annual %=(daily[Jan 1st]+1)*(daily[Jan 2nd]+1)....about 252 days terms)-1.

In Java, you could use this function. Pass in a daily time-series of returns.

    public static List<Tuple2<LocalDate,Double>> calcAnnualReturns(List<LocalDate> date, List<Double> values) {
List<Tuple2<LocalDate,Double>> list = new ArrayList<>();
int lastYear=-1;
BigDecimal tally=BigDecimal.ZERO;
if( values.size()>0 ) {
for (int i = 0; i < values.size(); i++) {
LocalDate ldt=date.get(i);
double value=values.get(i);
if( i==0 ) {
tally=BigDecimal.valueOf(value+1);
}else{
if( ldt.getYear()>lastYear ) {
// calculate
tally=tally.subtract(BigDecimal.ONE);
// reset to new year
tally=BigDecimal.valueOf(value+1);
}else{
tally=tally.multiply(BigDecimal.valueOf(value+1));
}
}
//
lastYear=ldt.getYear();
}
// finish last value
tally=tally.subtract(BigDecimal.ONE);
}

return list;
}


You can take the log difference: log(price_12-31-2014)-log(price_01-01-2014)

You can calculate the simple rate of return as: (price_12-31 - price_01-01)/price_01-01

Apples and oranges.

S&P 500 index (your first link) is not the same as SPY (your second link) so the results of course need not be the same.

S&P 500 is a statistical index published by Standard and Poors, it is generally given as price change only, although as a supplement a total return version is available from Wilshire and others; these TR figures differ slighlty from each other depending on how you assume dividends are reinvested. But if not otherwise specified S&P 500 is a price only (no dividends) figure.

SPY is an actual investable ETF which tracks the S&P 500 stocks. The shareholders of SPY collect both price change and dividends, which are distributed once a quarter. Also some modest fees are subtracted. The return on SPY is a good measure of achievable total return including realistic costs.

So it is not surprising that your second figure is about 2% higher than the first: the dividend yield on American stocks is about 2%!

• Thanks, and how to get annual return from daily prices? Is there is something wrong with the way I wrote? Why use log? Also I saw some using formulas like (1+r)=(1+r)*(1+r)... Thanks, – michael Mar 20 '16 at 23:44