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Stocks are often characterized by their P/E ratio. In principle, stock ownership represents part ownership of the company, but in practice shareholder are somewhat distanced from the earnings: The company may not pay dividends, growth of the company may not reflect to share price due to being buffered by speculative movements, and so on. However as is commonly held the P/E is still a useful tool to compare stocks to each other.

Can we also compare different assets to stocks in this way? For instance, can I calculate the P/E of a house by taking the price to own it (perhaps deducting repairs and fees), and dividing by the rent (let's assume the house is being rented out for profit)?

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In the long run (how long?) a shares price always reverts to being its proportional amount of the company's residual equity plus the net present value of its expected future cash flows. Or at least that's the theory.

In practice PE ratio is used not as a way of measuring what the stock price itself will do but what the fundamental value of holding that share is compared to its price. It is a way of measuring what a company is worth compared to its price and comparing it against other companies to find companies where the underlying value of the company is underrepresented by the price.

Comparing PE ratios within the same industry or sector is the most valid use for this (other than comparing previous years of the same company) and the validity of the comparison drops as the structure of the firm you are comparing with gets more different to that of the company. Each industry has its own "typical" average PE ratio and these differ wildly between industries so in a great many cases even comparing PE ratios between similar stocks in different industries isn't valid.

Any weird pseudo PE ratio that you create for other instruments will be meaningless. In general the best way to compare investments across multiple instruments is by comparing returns. when comparing stocks to other instruments you may want to use the return on stock price or the return on capital employed (ROCE) depending on whether you want to compare the trading performance or the fundamental performance.

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Yes, there are non-stock analogs to the Price/Earnings ratio.

Rental properties have a Price/Rent ratio, which is analogous to stocks' Price/Revenue ratio. With rental properties, the "Cap Rate" is analogous to the inverse of the Price/Earnings ratio of a company that has no long-term debt.

Bonds have an interest rate. Depending on whether you care about current dividends or potential income, the interest rate is analogous to either a stock's dividend rate or the inverse of the Price/Earnings ratio.

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