Bull markets are good for investors who own long stocks. And covered calls are good for creating monthly income. Buy why would you set a limit on your upside (by writing a covered call) when stocks are rising? Well, there are a few reasons. Maybe you are investing around a news event? Or trading on margin? There are legitimate arguments to be made for increasing your safety net and taking a possibly smaller gain. Here are some of the reasons why you may want to consider writing covered calls as stocks are going up:
Take some gains. After a nice run up in stock price it is wise to either reduce your position, or write some calls against your position so that if the stock gives back some of its gains you can capture some from the call premium. These two points can be combined by writing covered calls that are ITM (in the money) on the portion of the stock you were planning on selling anyway, as a way to get a bit more profit from the position. Or, if you're still very bullish then try selling some near-term OTM (out of the money) calls.
Monthly income. If you have core holdings that you are planning to own for a while then why not write some out of the money calls on them to generate some income (even if they're rising in a bull market)? Depending how far out of the money you choose, you may need to sell several months worth of time instead of near-month (to cover the commissions for the trade).
Velocity trade. Perhaps a stock has risen dramatically recently and the momentum investors are increasing. That activity usually increases the call premiums to a point where they're just too rich to ignore. In cases like this you may want to use DITM (deep in the money) covered calls. But be careful -- these momentum stocks can be volatile so it is best to keep the durations short (i.e. sell the near month, and not many months out).
News. Prior to a scheduled product or earnings announcements it is typical for the option premiums to increase. But instead of buying into the anticipated news, consider selling the excitement by writing a covered call. The amount that the option is OTM or ITM (out of the money or in the money) should match your thoughts on which way the news will go.
Borrowing. Using margin to trade stocks can be dangerous. You can experience quick losses if there is a sudden move against you. One way to increase your safety net is by writing DITM (deep in the money) calls against your holdings. You may still have losses if there is a fast move down, but the time premium and intrinsic value should buy you enough time to close out the position if you need to with smaller losses than if you had just held the stock outright.
Additional details on intrinsic value can be found at Born To Sell, a web site dedicated to covered call investors. The site includes a free covered call tutorial which talks about how time premium of an option should be sold.