How to calculate annual returns from daily prices?

Question

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,

Answer 1

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);                                                   
                    // add result
                    list.add(new Tuple2(LocalDate.of(lastYear, 12, 31), tally.doubleValue()));
                    // 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);                                   
        list.add(new Tuple2(LocalDate.of(lastYear, 12, 31), tally.doubleValue()));          
    }

    return list;
}

Answer 2

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

Answer 3

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%!