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I would like to compare the interest rate with the yearly return of a stock A and plot the 2 lines into 1 graph.

The interest rate, which is also a yearly return, is on any given date determined by the central bank. Say that I know that the interest rate is 3% on 1st of Jan 2000. So then I plot 3% for the 1st of Jan 2000.

Which yearly return of stock A should I then plot to make the comparison with this interest rate proper? Some options that I have thought of are:

  1. $\mathrm{yearly return(1 Jan 2000)= \frac{(stock index, 1 Jan 2000)- (stock index, 1 Jan 1999)}{stock index, 1 Jan 1999}}$

or:

  1. $\mathrm{ yearly return(1 Jan 2000)= \frac{(stock index, 1 Jan 2001)- (stock index, 1 Jan 2000)}{(stock index, 1 Jan 2000)}}$

Which of these methods is the correct way, or do you propose something else?

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  • $\begingroup$ This sounds more appropriate for the Personal Finance and Money SE $\endgroup$ – xan Apr 30 '15 at 14:37
  • $\begingroup$ @user3697176 post that as an answer! $\endgroup$ – shadowtalker May 4 '15 at 12:58
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Interest rates are forward rates; they apply from that day forward.. So you should also use forward rates for the stocks, i.e., the second equation. Note, however, that the rate of return on stocks will change from day to day, while the bank rate is constant over longer periods.

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