Realized Returns

Example: Stock price and dividend data of Microsoft stock

Question

1. Suppose you purchased MSFT on Nov 1, 2004 and sold it immediately on Nov 15 after receiving the divided. What was your realized return?

Realized return (non-annual holding period) is the total return that actually occurs over a particular time period (no interim cash flows):

$$R_{t+1}=\frac{Di{v}_{t+1}+P_{t+1}-P_t}{P_t}=\frac{3.08+27.39-28.08}{28.08}=0.0851=8.51\%$$

Dividend yield is given as

$$\text{Dividend yield}=\frac{3.08}{28.08}=10.97\%$$

Capital gain yield is given as

$$\text{Capital gain yield}=\frac{-0.69}{28.08}-2.46\%$$

Question

2. Suppose you purchased Microsoft stock (MSFT) on Nov 1, 2004 and held it for one year, selling on Oct 31, 2005. What was your annual realized return?

• If you hold the stock beyond the date of the first dividend, then to compute your return, you must specify how you invest any dividends you receive in the interim.
  • Let’s assume all dividends are immediately reinvested and used to purchase additional shares of the same stock or security.

If a stock pays dividends at the end of each quarter, with realized returns $R_1,\dots R_4$ each quarter, then its annualized return, $R_{\text{annual}}$ is computed as the compounded period returns:

$$1+R_{\text{annual}}=(1+R_1)(1+R_2)(1+R_3)(1+R_4)$$

In the case of MSFT:

$$\begin{array}{rl}1+R_{\text{annual}}& =(1.0851)(0.9496)(0.9861)(1.0675)(0.9475)=1.0275\\ R_{\text{annual}}& =2.75\%\end{array}$$

Notes:

• Selling price is lower than purchase price, but the return is positive because of dividends. Total return is 2.75% over the year.
• MSFT stock price fluctuated up and down over the year. Returns are risky. Realized return is not possible to be predicted.
• However, from the observed realized returns over many years, we can graph the distribution of actual returns and calculate a historical average return which can be used as an “expected” return.