Proper way to annualize returns

Searching for "how to annualize interest rates" on Google leads to the following results:

1. Wikihow's How to Annualize a Percentage
2. Investopedia's Annualized Rate of Return

Wikihow

Recommends the following formula:

Year-to-Date Return = Percentage Return * Time Factor

Where:

• Percentage Return = how much you made as a percentage since Jan 1
• Time Factory = 365 divided by the number of days since Jan 1

Investopedia

Recommends this other formula:

AP = ((P + G) / P) ^ (365 / n) - 1

Where:

• AP = Annualized Performance Rate
• P = principal, or initial investment
• G = gains or losses
• n = number of days

Example

Suppose that I started with \$10k, made a non-compounded return of 10% and today is Mar 15 (so that 73 days passed since Jan 1). Using the formulas above I would get two different answers:

Roi_Wikihow = 0.1 * 365 / 73 = 0.5 = 50%
Roi_Investopedia = ((\$10,000 + \$1,000 / \$10,000) ^ (365 / 73) - 1 = 0.61051 = 61%

Question

It seems to me that Wikihow's approach doesn't compound the returns, whereas Investopedia does. That is, the former calculates an APR (annual percentage rate), whereas the latter calculates an APY (annual percentage yield). Is this correct?

Yes, the difference between the two formulas is based on whether the investment is compounding or not. Your first link states this:

Take note that the effective annualized rate will depend on how often the interest compounds.

For example, if you buy a stock that pays a 5% dividend and each quarter you withdraw and spend it for living expense, your ROI remains the same. OTOH, if you reinvested the dividend, you'd achieve compound growth. Hence the reason for two different formulas.

• Thanks for confirming! My confusion arose primarily because of Investopedia defining "AP" as "Annualized Performance Rate". Feb 13 '21 at 13:41

I use Excel's built-in =RRI() function: "Returns an equivalent interest rate for the growth of an investment."

In your case, =RRI(73,10000,11000) = 0.13065% compound growth per day. Multiply that by 365 to get 47.69% CAGR.

Then I verified that with =10000*(1+0.13065%)^73, the answer to which is \$11,000.02`.

• Thanks for the tip! RRI looks interesting, but I don't think it applies to my example. The return of \$1000 over the 73 days is supposed to be not-compounded, i.e. earned on Mar 15, not daily. Feb 13 '21 at 13:43
• @PaulRazvanBerg but you want to Annualize the Return. This annualizes the return. (Note that, compounded daily, a CAGR of 4.88% yields 5.00%). Feb 13 '21 at 14:03