Value-at-Risk and dividend payments

Question

How should dividends be considered when computing Value-at-Risk for a stock portfolio using Historic data.
To simplify let's consider a very simple portfolio of one long position on a stock. My VaR model setups is also very simple:

• I have returns for the stock for the past 500 days
• I then take the empircal distribution and call my 99% VaR as the 5th "worst" scenario

But how should I include the dividend payments for the stock? This question can be boiled down to: How should I take dividend payments into account and construct a new return series for the stock?

I have been considering to override the return at dividend payment days the following way:

$$\hat{r}_t=\frac{P_t+DVD-P_{t-1}}{P_{t-1}}$$ $\hat{r}_t$ is the new return. Are there any valid arguments that is is not a good way to tackle the problem mentioned above?

Answer 1

You are right, one should consider returns that are adjusted for dividends payments (if you go for arithmetic returns, then it's your $\hat{r}_t$).

The argument here is that this is the real return you get, because the dividend amount is detached from the stock, but is not lost (you get it in cash).

EDIT: To complete with Antoine's excellent comment, the adjustment should be made on the ex-dividend date rather than on he payment date.