After six years of rising U.S. stock prices, investors are no doubt richer. But they may be thinking a little less clearly.

“In a bull market, there’s a tendency for investors to think they’re brilliant,” says Brad Barber, a finance professor at the University of California, Davis, and an expert in behavioral finance. Indeed, as share prices climb, investors’ confidence grows and they start making all kinds of dubious claims.

Here are seven comments you have probably heard from friends—and that may have escaped your own lips.

1. “I’ve beaten the market.”

Investors often compare their global stock portfolio to the S&P 500, an index of U.S. large-company stocks. That’s an easy comparison in a year like 2015, when stocks in foreign countries and shares of smaller U.S. firms are outpacing the S&P 500.

The better performance of foreign and small stocks can boost a portfolio’s return, so it beats the S&P 500—even if the portfolio isn’t beating an index that tracks the global stock market.

If the S&P 500 doesn’t provide a favorable comparison, investors will often change indexes or ignore one-year results and instead focus on three-year or five-year returns.

Or they might not use an index at all—and instead compare their results to the mediocre actively managed mutual funds their brother-in-law bought.

2. “My stock picks have made so much money.”

Share prices have tripled since 2009, so anybody who owned stocks over the past six years should have notched healthy gains. “But we ascribe the gains to our own skill,” says Mr. Barber.

This has an upside: Self-confident individuals are often happier. Problem is, they also tend to trade too much and make big, undiversified investment bets.

That tendency can get worse as stocks climb higher, according to Mr. Barber. Investors not only grow more cocky as their portfolios grow fatter, but also they feel as if they’re ahead of the game. Like casino gamblers who are lucky early in the evening, “you get this ‘house money’ effect,” he explains. “You’re willing to take on more risk, because you feel like you’re playing with gains.”

3. “It’s the Fed’s fault.”

What happens when our investments don’t pan out? Instead of blaming ourselves, we blame others.

“When our bond portfolios have done well in recent years, it’s because we made good decisions,” says John Nofsinger, author of “The Psychology of Investing” and a finance professor at the University of Alaska Anchorage. “But when it comes to the bond market’s recent bad performance, we blame the Fed.”

Bonds have struggled over the past month, as the yield on the benchmark 10-year Treasury note has climbed from below 1.9% to above 2.2%, driving down bond prices.

Alternatively, we might simply rewrite history. “We misremember to make ourselves feel better,” Mr. Nofsinger says. “We just ignore the fact that our 401(k) didn’t do that well last year.”

4. “My portfolio has grown so much.”

That may be true. But how much of the growth has come from the savings we have added, rather than from investment gains?

If we’re disappointed by our investment performance, “we can change from measuring investment return to investment level,” Mr. Nofsinger says. “If my return is negative but contributions allowed the level to still increase, I can focus on the level.”

5. “It’s only a paper loss.”

If we buy a $10 stock that falls to $8, we have lost money. But many investors don’t see it that way.

“People feel that paper losses are different from real losses,” notes Meir Statman, a finance professor at California’s Santa Clara University and author of “What Investors Really Want.” The reason: There’s still a chance that the shares will bounce back.

What happens when we finally sell that losing stock? We quietly drop it from our mental arithmetic—and now we can boast to our neighbors that we’ve made money on every stock we own.

6. “I bought it for diversification.”

When an investment doesn’t perform the way we expect, we will often mentally reclassify it. Take gold, which was all the rage after its price jumped more than sevenfold over the decade through 2011.

But instead of continuing to soar, gold has lost more than a third of its value since September 2011. What to do? We might drop it from the “it will make me rich” portion of our portfolio—and reclassify it as “it might do well if we get another financial crisis.”

7.“This time, I’ll get out before the crash.”

In hindsight, market tops and bottoms seem obvious, so we figure we’ll see the next one coming. But the current bull market’s peak will probably be just as murky as the low point of the last bear market, in March 2009.

“We can now see that that was the bottom of the market,” Mr. Statman says. “But at the time, you couldn’t see the pattern.”

Jonathan Clements is the author of the “Jonathan Clements Money Guide 2015.” Email: ClementsMoney@gmail.com