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If you are looking for stocks that appear to be on sale while the market is trading near all-time highs, you'll probably have to buy companies facing some kind of headwind. That's not unusual. Virtually every business goes through tough times eventually. But it does require a bit more resolve to buy discounted stocks instead of the ones that Wall Street loves.

If you have the stomach for some contrarian buys, consider these two Canadian stocks: Toronto-Dominion Bank (NYSE: TD) and Bank of Nova Scotia (NYSE: BNS). Both have high yields thanks to some current challenges, but their long-term prospects remain bright. Here's what you need to know.

Toronto-Dominion Bank fumbles the ball

It certainly hasn't been an easy time lately for Toronto-Dominion Bank. The stock is off nearly 15% so far this year. That's probably thanks to multiple financial probes into potential money laundering by bank employees in New York and Florida. TD Bank (as the company is often called) likely should have had better controls in place.

But it didn't, and now it is paying the price, which has included the scuttling of an acquisition, additional costs to upgrade internal controls, and potentially sizable penalties. The bank has already taken a $450 million provision for losses, and analysts estimate it could ultimately face as much as $4 billion in fines.

There's no way to sugarcoat any of this -- these issues are likely to hang over the bank at least for a little while as it works with regulators to address issues and rebuild trust.

But it probably won't be the end of its long-term growth, just a pause. After all, Toronto-Dominion is one of the largest banks in Canada and also has a significant East Coast presence in the United States. After it works through the current issues, it should be able to get back to expanding in the U.S. market.

For now, TD Bank is likely to be stuck in neutral. A falling stock price has pushed up the dividend yield to a historically high 5.3%. The average bank in the United States has a yield of around 2.8%, using SPDR S&P Bank ETF as a proxy. If you can stomach taking on a little regulatory risk, you can nearly double the yield you collect from a bank stock here.

Bank of Nova Scotia is getting focused

Bank of Nova Scotia, or Scotiabank, has a different problem. It has been an industry laggard on key metrics like earnings growth, non-interest revenue growth, and return on equity. That's left investors with a sour taste in their mouths -- and the stock trading with a huge 6.6% dividend yield. What's the problem?

Unlike most of its Canadian peers, which have focused on the U.S. market, ScotiaBank has attempted to find growth in South America. That's an inherently riskier decision given that South America is largely driven by developing markets, which are more volatile than developed markets like the United States.

Clearly, Scotiabank's plan hasn't worked out quite as well as hoped, but it is adjusting by focusing on the best opportunities (Mexico) and considering plans to exit less attractive ones (Colombia). This is a multi-year turnaround effort for sure, but it is a good thing that Scotiabank isn't sticking its head in the sand.

What's important to remember here, however, is that Canadian banks are generally pretty conservative due to heavy regulation in their home market. So while Scotiabank is trying to grow its business in a riskier area of the world, it isn't going out on a financial limb to do it.

Scotiabank remains a very strong bank and is actually working on increasing its resilience. Its Tier 1 capital ratio, a measure of a bank's ability to deal with adversity, rose nearly a full percentage point year over year to 13.2% in the second quarter of its fiscal 2024. That's well above the regulatory minimum and positions the Bank well to soldier on through its business overhaul. If you have the stomach for it, you can comfortably collect the outsize yield while it does.

Not perfect, but probably worth a look

While there are very clear reasons why investors might want to avoid TD Bank and Scotiabank, the truth is that these companies have survived the market's -- and the banking sector's -- ups and downs for more than 100 years. If you are a long-term investor willing to take on a little extra risk to collect a big dividend check, the balance between risk and reward here looks tilted in your favor. You'll just have to stomach a little uncertainty while you wait for better days.

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Reuben Gregg Brewer has positions in Bank Of Nova Scotia and Toronto-Dominion Bank. The Motley Fool recommends Bank Of Nova Scotia. The Motley Fool has a disclosure policy.

The views and opinions expressed herein are the views and opinions of the author and do not necessarily reflect those of Nasdaq, Inc.

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