# Deriving Beta

this might be silly but I cant get it through my head. In question 39 on book 6 test 2 am. they derived beta as corr. of A and MKT * std of a / std of MKt = beta Please drop your \$.02 here. thanks.

Beta = Cov (i,m) / Variance M Cov (i,m) = corrl of i ,m x std dev of i x std dev of M substituting Beta = corrl of i , m ( std of i/std of M)

Try this way of thinking about it. What does Beta tell you? Answer: How much of the market risk a stock is exposed to. Low Beta means a stocks moves up and down less than the market. High Beta means the opposite. So you have the formula: Beta = Corr(A to Mkt) * Std Dev(A) / Std Dev(Mkt) What would it take to make this formula equal to one? A correlation of 1 and a standard deviation of company A equal to the standard deviaion of the market. If the correlation goes down, so does Beta because company A doesn’t move with the market as consistently (because it is less correlated!). If Std Dev(A) goes down relative to the Std Dev(Mkt) Beta will decrease because company A is less “risky” (defined as standard deviation) than the market is. So just think of the two things that decrease Beta when they go down and put them in the numerator. Think of the thing that increases Beta when it goes down (market risk/std deviation) and put it in the denominator. Hope that helps.

Dwight thanks for the conceptual answer to my confusion, your time is much apreciated. Thanks rajiv75 too.