According to CAMP formular E(R_{i}) = R_{F} + β_{i}[E(R_{M} − R_{F})]. Sometimes the book call E(R_{i}) as the required rate of return or expected return, so are they the same? when I do some reasearch online , the definition of expected return and required rate of return are different?

If I have E(R_{i}) = 5%, ( stock price $100) and the forcast market rate is 10% ( stock price $50) , is the stock overvalued or undervalued? I am confused because I think that the required rate is the intransic value ( the true) value while the market is just the forecast. So it should be undervalued , why overvalued?

I don’t know what you mean by stock price $100, then stock price $50!

My understanding is that expected and required in this context are same. If E® = 5% and forecasted R=10%, the stock is undervalued because its forecasted return exceeds the required rate of 5%.

it is just assumed that the Rate is high then the price is low and vice versa. what is the rationale that forecasted return exceeds the required return then the stock is undervalued?

how is the price (value) calculated? it is by discounting cash flows at the rate.

when rate increases (forecasted return) -> the price will go lower - so the stock will be undervalued when compared to what it is now … (which is at the expected return).

Let s try it like this. You ran your own forecast and you came up with an expected return of 10%. Now what? Is that good or bad? CAPM says that this stock, based on its beta and the expected return for the market as well as the risk-free rate, should return about 5%…notice, CAPM doesn’t say what the current stock price is. It is simply telling you that this stock should return 5% on average. But you just calculated a higher return based on where the stock is currently trading. Let us say the current price is $100, so you believe it will be $110. That means if you had a “real-time” CAPM, it would say the stock price right now should be $104.76 (which is the price that will become $110 if you get a 5% return). Therefore, the current stock price of $100 is undervalued because according to CAPM it should be $104.75.

That’s the actual way of thinking about it, but you can make up your own short cut.

market rate minus risk free rate is market risk premium. it is the rate you use in CAPM to calculate required rate. therefore, you use required rate to discount your cash flows. you cannot simply compare market rate and required rate - you need to take beta and risk-free rate into consideration.

I am still confused about the concept of overvalued and undervalued stock. now if CAPM says the required return is 5% and the market say the rate should be 10% , why this stock is undervalued?

To find the price of the stock, I take the dividend and divided by requred rate compared with the market price dividend divided by market rate, since the rate from CAPM is less than market rate ( 5%<10%) , so the price from CAPM is higher than the price from market. how come is undervalued?

Again the problem with understanding this is that some of yo think CAPM is a dynamic formula, it is not. If it says the expected return is 5%, does that mean you get 5% anytime you buy the stock? If the stock has already shot up 20%, CAPM would still say the return is 5%…now think about that and read what I wrote above to get the exact idea. Ignore the discounting stuff mentioned above, that’s irrelvant, you can use any method to forecast the return, even invent your own if you want.

you are thinking way to hard about this. Use the CAPM to discount your cash flows. That is your intrinsic value.compare this to the market value of the stock and determine if it is over or underpriced

Let us try that. Since CAPM return is 5%, when you discount, you will get a larger number than if you used 10%, so your conclusion will be that the stock is overvalued, not undervalued as it should be.

wow this thread is painful to read. clearly the OP needs to review definition of concepts (RM vs Ri). I re-read your posts Cfapassforsure and clearly you are quite confused. I don’t think i want to add to the confusion here.