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Are they the same thing?

Is yield the annualized return rate?

Why when yield rise, yearly return increases but price falls?

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They are related, but not the same thing.

The yield associated with an asset is the ratio of the (usually annual) return produced by that asset to its price: $$\text{Yield (%)}=\frac{\text{Annual Return (\$)}}{\text{Price of Asset (\$)}}.$$

Simple case: when yield = interest rate

An interest rate is an example of a yield. For example, suppose a bank account pays an interest rate of x% p.a. That means that \$100 deposited in the account today would become \$(100+x) in a year's time. The annual return is therefore \$x. We can plug these numbers into our formula to calculate the yield: $$\text{Yield}=\frac{\$x}{\$100}=x\%.$$ In this example the yield is just the interest rate, so the two coincide.

More complicated case: yields and asset prices

Things get a little more complicated when the interest rate is fixed but the price of the asset can change over time.

For example, the government issues bonds when it needs to borrow money. Each bond has an initial price and a set annual return (known as the coupon payment) that does not change over the entire life of the bond. Suppose that we have a bond that initially costs \$100 and has a coupon payment of \$5 (meaning that you get \$5 for each year that you hold the bond). We can check the bond's coupon yield: $$\text{Coupon Yield}=\frac{\$5}{\$100}=5\%.$$ This is, again, just like an interest rate.

Now, though, suppose that banks start offering an interest rate of 10% on an ordinary savings account. Suddenly, your bond's 5% doesn't look so great! But the \$5 coupon payment can't change—it is permanently fixed when the bond is created. People are therefore going to want to try to sell their bonds to get their money back so that they can put it into a bank instead. As per normal supply & demand logic, lots of people selling bonds is going to make the price of bonds fall. So now you can buy a bond for, say, \$80. That means the yield has changed! $$\text{Current Yield}=\frac{\$5}{\$80}=6.25\%.$$ Alas, people are still going to be reluctant to buy the bond because it still has a lower yield than the bank account—so the price is going to have to fall even further. Eventually, the price of the bond falls to \$50, at which point $$\text{Current Yield}=\frac{\$5}{\$50}=10\%.$$ Now the bond and bank account have the same yield (meaning that someone with money to invest would get the same return from either). People are now indifferent between holding the bond or a bank deposit and equilibrium is restored.

In practice, things are a little more complicated because people compare the returns on bonds to all kinds of assets—stocks, real estate, etc. But the principle is the same: the price of the bond adjusts to ensure that the yield on the bond is in keeping with the risk-adjusted return available elsewhere.

A final note: yields where there are no interest payments

The last important reason why we distinguish yields from interest rates is that some assets don't have any interest rate to speak of, but it nevertheless makes sense to talk of a yield. One example is stocks—there is no interest payment on such assets, but the board may decide to return some of the firm's profits to investors in the form of a dividend. A dividend is an amount that is paid to investors for each share that they hold. We can use the dividend to calculate a yield just as though it were an interest rate:$$\text{Dividend Yield}=\frac{\text{Dividend (\$)}}{\text{Stock Price (\$)}}.$$

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  • $\begingroup$ I think the numerator in your first equation should be $Annual Income$ not $Annual Return$. Because returns look backward and yields look forward. Also, returns take into account price appreciation (or depreciation) of the asset. And yields do not. $\endgroup$ – FreeMarketUnicorn Jul 14 '16 at 8:02

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