### On price-to-earnings and price-to-rent ratios

Standard metrics for assessing values of stocks and homes are the price-to-earnings ratio and price-to-rent ratio. For stocks, sometimes a price-to-dividend ratio is used. Also for stocks, since earnings and dividends can be highly volatile in the short-run, a longer-run average is used rather than current earnings or dividends.

Here's a recent chart from Calculated Risk showing the price-to-rent ratio for houses.

And here's a recent chart from Econbrowser showing the price-to-earnings ratio for stocks.

(Note that the first plot shows the index rescaled so that~~1980~~ [1987] = 1. If it were not rescaled this way, the units on the vertical axis would look pretty similar to those for stocks.)

These are nice metrics both conceptually and empirically.

Conceptually, they say something about the rate of investment return. If the stock were infinitely lived and paid same earnings, then the net present value of the flow of earnings equals the price if future earnings are discounted at a rate equal to the inverse of the P/E ratio. For example, a P/E ratio of 20 means the current price is equal to forever receiving current earnings discounted at a rate of 5% (1/20). For houses it's much the same, since rent represents the earnings from a house.

Empirically, these ratios tend to revert to their means over the long run. Thus, if the P/E ratio gets way above its historical mean it can indicate a bubble. So when P/E ratio is above the historical mean, some say prices are too high and when the P/E ratio is below the historical mean some say it's a good buying opportunity. Over the long run (10-20 years), returns are in fact much higher the lower the P/E ratio, a fact pointed out by Robert Shiller some 30 years ago that has withstood test of time.

Okay, that's the standard story. The problem is that there are two other key factors to consider:

1) How much does one expect earnings to grow or decline in the future?

2) How do current interest rates compare to the historical average?

When examining the

But (2) can be hugely important. After all, if you're not putting your money in stocks or a homes, where are you going to put it? If interest rates are very high, you need a higher return (lower P/E ratio) to make investing in a home or stocks worthwhile. If interest rates are low, a higher P/E ratio may still be a good investment opportunity.

The problem is that (2) gets unduly ignored. This matters right now because if you do not account for (2), home and stock prices still look a little high--the P/E ratios, while well off their peak bubble highs, are still a bit above historical averages. But if you account for the fact that interest rates are at historical lows, the P/E ratios look very attractive. One place this is captured is by the housing affordability index--it's about as high as it's ever been.

In my view the right way to gain a quick assessment of whether current prices make sense is to instead look at an index of the P/E ratio divided by the inverse of the 10-year T-bill rate (after all, stocks and houses should be long-run investments). I suspect that index would show today's index value to be quite low by historical standards, and thus a good time to buy.

If I find the time I'll try to put that index together on another day.

Maybe some homeowners wouldn't be willing or able to do this. But to those willing and able, buying a house at today's prices and interest rates represents a fantastic long-run investment opportunity. WAY better than cash, buying bonds (especially in you think interest rates will rise), and probably even better than buying stocks.

The only good reason not to buy right now is because you think prices will fall further. While that's a real possibility, it's also the same kind of thinking that led to the bubble in the first place.

Here's a recent chart from Calculated Risk showing the price-to-rent ratio for houses.

And here's a recent chart from Econbrowser showing the price-to-earnings ratio for stocks.

(Note that the first plot shows the index rescaled so that

These are nice metrics both conceptually and empirically.

Conceptually, they say something about the rate of investment return. If the stock were infinitely lived and paid same earnings, then the net present value of the flow of earnings equals the price if future earnings are discounted at a rate equal to the inverse of the P/E ratio. For example, a P/E ratio of 20 means the current price is equal to forever receiving current earnings discounted at a rate of 5% (1/20). For houses it's much the same, since rent represents the earnings from a house.

Empirically, these ratios tend to revert to their means over the long run. Thus, if the P/E ratio gets way above its historical mean it can indicate a bubble. So when P/E ratio is above the historical mean, some say prices are too high and when the P/E ratio is below the historical mean some say it's a good buying opportunity. Over the long run (10-20 years), returns are in fact much higher the lower the P/E ratio, a fact pointed out by Robert Shiller some 30 years ago that has withstood test of time.

Okay, that's the standard story. The problem is that there are two other key factors to consider:

1) How much does one expect earnings to grow or decline in the future?

2) How do current interest rates compare to the historical average?

When examining the

*overall*market, not an individual stock or individual house, I think (1) is a pretty small issue. In aggregate, earnings or rents tend to be pretty steady or mean-reverting--there's typically no good reason to expect the future trend to be much different than the past.But (2) can be hugely important. After all, if you're not putting your money in stocks or a homes, where are you going to put it? If interest rates are very high, you need a higher return (lower P/E ratio) to make investing in a home or stocks worthwhile. If interest rates are low, a higher P/E ratio may still be a good investment opportunity.

The problem is that (2) gets unduly ignored. This matters right now because if you do not account for (2), home and stock prices still look a little high--the P/E ratios, while well off their peak bubble highs, are still a bit above historical averages. But if you account for the fact that interest rates are at historical lows, the P/E ratios look very attractive. One place this is captured is by the housing affordability index--it's about as high as it's ever been.

In my view the right way to gain a quick assessment of whether current prices make sense is to instead look at an index of the P/E ratio divided by the inverse of the 10-year T-bill rate (after all, stocks and houses should be long-run investments). I suspect that index would show today's index value to be quite low by historical standards, and thus a good time to buy.

If I find the time I'll try to put that index together on another day.

**Update**: Here is Calculated Risk making the argument that houses are NOT cheap. I disagree. In the case where interest rates do rise to 7% in a few years (not something the market expects at all), home prices fall, and the owner wants to move, s/he can always rent the house out for well above the mortgage payment are receive a decent income from the difference (assuming s/he's takes out 30-year fixed mortgage at today's low interest rates) while continuing to steadily pay down the principal. If interest rates rise to 7%, rents will rise too, and at today's price-to-rent ratio, rent is already close to the mortgage payment on the first day of the mortgage.Maybe some homeowners wouldn't be willing or able to do this. But to those willing and able, buying a house at today's prices and interest rates represents a fantastic long-run investment opportunity. WAY better than cash, buying bonds (especially in you think interest rates will rise), and probably even better than buying stocks.

The only good reason not to buy right now is because you think prices will fall further. While that's a real possibility, it's also the same kind of thinking that led to the bubble in the first place.

the most recent two posts on your blog are much closer to what I expect from an economics blog. Stick to these type topics and I believe you will have a much broader audience than some of your earlier posts (ie, "obama is not elusive")--just an opinion

ReplyDeleteThanks for you comment, Anonymous (not even a pen name?)

ReplyDeleteIs it so much for an economist to ask that people judge politicians by their policies rather than insignificant, vague (and totally unsubstantiated) accusations of elusivity?

Is it so much for an economist to ask that people judge politicians' policies according to the constraints politicians face?

And with regard to the implicit message of that post--about a media that has a strong incentive to incite conflict and pander to the prior beliefs of their own constituencies rather than inform them--is there not enough economics worth blogging about?

My goal here is to keep a record of my own thoughts so I can look back one day and (a) see how Obama pulled one over on me and/or (b) recall the events sentiment from which things progressed.

oh yeah, i also was a big fan of cochrane's tips for empirical work..courtesy of mankiw I guess, but still, i don't always make it over there and wouldn't have stumbled on it--great post

ReplyDeleteAs a closet finance nerd I feel obliged to point out that the numerator ("P") isn't a complete representation of the market's assessment of the value of one or many companies, because the equity holders only have claim to the residual cash flows after debt is paid. This is relevant when calculating implied discount rates (as you did above), and also because P/E could fluctuate with levels of corporate debt even if earnings expectations and discount rates remained fixed.

ReplyDeleteOne example of a better ratio is EV/EBITDA, where EV = entity value = equity + debt, and EBITDA is a more accurate measure of the operating earnings of a company... but of course this is harder to calculate and thus less widely used.

Also, a cautionary note on your investment implication that buying a house now is likely a better investment than buying stocks or bonds: buying a single house (or stock) is a lot riskier than buying the market average, because while earnings/rent is probably reliably mean-reverting in aggregate (your point #1), this is no longer the case if you're concentrated in a few individual assets.

ReplyDeleteThanks R. I don't dispute you on either count.

ReplyDeleteYeah, buying a house (or stocks) is risky. But at least historically the reward long-term has been well worth it. This last decade has been the exception. I'd be really surprise if that happened back-to-back.

Put another way: A bet against houses or stocks right now is a bet that interest rates will fall further. To me, that is very hard to imagine.

I agree on aggregate, but isn't buying a single house analogous to buying a single stock, which is a much worse investment strategy than buying a market-wide stock index? Maybe individual houses are more correlated with the housing market than individual stocks are with the stock market, but it still seems very concentrated (rather than diversified) as an investment strategy, which increases risk.

ReplyDelete