One way to earn a second income is to build a portfolio of blue-chip stocks that pay dividends.

The amount an investor should invest to achieve a particular goal depends on several things. One of them is the potential dividend yield at the time of investment. Another question is whether the potential yield will ultimately be achieved. After all, no dividend is ever guaranteed.

Understanding the Role of Dividend Yield

Let’s start with yield.

At a 10% return, a second annual income of £5,000 would require investing £50,000. At a 7.5% return it would take £75,000. With a 5% return, the amount required is £100,000.

So, does it make sense to just invest in 10% producerssuch as FTSE100 insurer Phoenix (LSE: PHNX) ?

Maybe – but maybe not.

Investing purely on the basis of yield is child’s play. Dividends can be reduced or canceled – so the possible the current yield may end up being very different from the real performance in the future.

That said, I might be interested if a good company selling at an attractive price also offers a high return. I don’t invest just because of the performance. But I wouldn’t be put off by a high yield either.

In fact, it might make the stock more attractive to me when it comes to building a second income.

Quality above all

Phoenix is ​​a good example of this, as it’s a stock I think investors should consider.

The company operates in a large and complex market. This complexity poses a barrier to entry, even though there are still many competitors in the insurance market.

But Phoenix has many advantages. One of them is its large customer base, which numbers around 12 million people. Another reason is its collection of trusted brands, including Standard Life and SunLife. It also has a proven business model that has helped support annual dividend growth in recent years, a feat the company intends to replicate in the years to come.

No stock is without risk, and a double-digit return makes me wonder if I’ve missed something that other investors consider a significant risk.

One of my concerns is the impact that any downturn in the housing market could have on the valuation assumptions used in Phoenix’s mortgage portfolio. If these assumptions were to be revised, it could be bad news for earnings.

Spread the risk

Overall, though, I see a lot of upside to the investment case for Phoenix.

But things can change, so no matter how much I like a stock, I always keep my portfolio diversified. With the average FTSE 100 yield currently hovering around 3.6%, a yield of over 10% is exceptional. An average yield of 7.5% is, however, less exceptional.

I think I could aim for a second annual income of £5,000 by investing £75,000 in the current market. I don’t do it all at once, but keeping in mind the ISA allowancesI am progressing over time.