Share price gains aside, the good news is that both companies seem to be making slow but steady progress with their turnaround plans. There is some light at the end of the tunnel. Where things get difficult is in deciding whether each firm's valuation already reflects this potential.
After all, Tesco shares currently trade on 21 times 2017 earnings. Morrison looks a bit more reasonable, on 19 times 2017 forecast earnings, but both stocks look expensive relative to expected profits.
Although both stocks look much cheaper when compared to historical earnings, these may not be a realistic guide to what's possible in the future. Both supermarkets have cut their prices and their profit margins to try and win back customers. Competition from Aldi and Lidl means that none of the big players are able to make big gains in market share.
Look beyond earnings
The price/earnings or P/E ratio is the most common way to value a stock, but it's not the only one. Using alternative ratios can often reveal information which the P/E ignores.
For example, Morrison's results highlight the firm's strong free cash flow generation. Based on last year's figures, Morrison shares now trade on just 9 times free cash flow. That's a very attractive valuation, as it suggests that the shares are cheap relative to the surplus cash Morrison's business is generating.
Morrison also has an attractive property portfolio, much of which is freehold. Last year's figures show that Morrison has tangible net assets worth 140p per share. This provides a decent level of asset backing for the firm's 200p share price, in my view. The firm's dividend yield is also worthwhile, with a forecast yield of 2.7% for the current year.
It's hard to make a direct comparison between Tesco and Morrison at the moment, because Tesco's 2015/16 results are not due until the middle of April. However, last year's figures suggest that neither cash flow nor asset backing will be as strong as Morrison's.
A difficult choice
Situations like this are quite common in investing, in my experience. A stock looks fully valued based on the available facts, but there are no obvious problems. The company is making good progress.
This leaves us with two options. One choice is simply to continue holding the shares until some bad news appears to justify a sale. In these situations, a firm's share price and profits often rise much further than expected before they start to stagnate.
A second choice is to try and predict the future. If you think that the supermarket sector will stay roughly as it is today, then it might make sense to sell. After all, if current forecasts are correct, Morrison and Tesco are already fully valued.
My decision -- for now -- is that I'm going to hold onto my shares in Tesco and Morrison. The decline of both supermarkets took two or three years, which was longer than many investors expected.
I reckon that a full recovery is also likely to take a little longer than expected.
Roland Head owns shares of Tesco and Wm Morrison Supermarkets. The Motley Fool UK has no position in any of the shares mentioned. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors.