After banks reported earnings last week, now it's time for insurance companies to step up for shareholders and analysts. Travelers Companies (TRV 1.51%) is among those kicking off earnings season for the insurance industry, and many more will follow next week.

But this company couldn't have gotten things off to a better start Travelers Companies delivered strong results all around, with both revenue and earnings beating analyst expectations. Results were solid across the board and driven by premium momentum, better net investment income, and robust underwriting gains.

1. Beating estimates
For the third quarter of fiscal 2014, Travelers Companies reported revenues of $6.9 billion, up 7%, which compares against revenues of $6.5 billion a year ago, and against analysts' revenue expectations of $6.6 billion.

The property and casualty insurance business also reported earnings of $2.69 per diluted share versus $2.30 per share last year -- a 17% increase. Analysts, on the other hand, expected the insurance company to deliver EPS of $2.26.

With beats on both earnings and a revenue, Travelers Companies has not only solidly beaten expectations, but has also proved to investors that it can sustain premium momentum. In Q3 2013, Travelers Companies reported net written premiums of $6.0 billion versus $5.7 billion, up 6% year over year, lending credibility to the assertion that insurance companies continue to see attractive top-line tailwinds.

2. Net investment income as a driver of business profitability
Insurance companies such as Travelers Companies basically make money two ways. First, they rake in insurance premiums and try, via prudent risk selection, to make a profit on their core insurance/underwriting operations.

Second, insurance companies invest their premiums in fixed income, equity, and alternative assets to achieve income from their investment portfolio -- income that, in turn, can be used to invest in operations, to offset underwriting losses, or to remunerate shareholders.

While most investors focus on traditional insurance metrics such as combined ratios, which are distinctly important in evaluating the performance of an insurance company's primary business, the net investment income can be extremely relevant for overall company profitability.

In the case of Travelers Companies, for instance, third-quarter net investment income accounted for the majority of its operating income before interest and taxes. Its net investment income of $719 million not only increased $62 million year over year, driven by non-fixed income returns, but it also exceeded Travelers Companies' quarterly underwriting gain of $564 million.

Source: Travelers Companies Q3 2014 earnings release.

3. Strong core insurance operation
Net investment income has made up the majority of Travelers Companies' operating income, but its insurance operations produced just as solid results.

For the third quarter of fiscal 2014, Travelers Companies reported a combined ratio of 90%, which is only slightly worse than last year's 88.9% but still gives the insurance company more than sufficient wiggle room.

More importantly, its core insurance operations contributed handsomely to its overall return on equity in the first nine months of 2014. The return component breakdown reveals that the core insurance business contributed 6.2% of Travelers Companies' total 14.8% return on equity, while the remainder, 8.6%, came from its investment portfolio:

Source: Travelers Companies Q3 2014 earnings presentation.

The Foolish takeaway
Travelers Companies beat the Street's earnings and revenue estimates and continued to benefit from strong underwriting gains as well as higher net investment income. In fact, its investment income improved by more than 9% year over year, driven by private equity returns.

Should investors see continued premium momentum and investment income in the coming quarters as well, Travelers Companies can give investors even more reasons to buy this already healthily performing insurance company.