A probability question from notes SS.2 reading 8

CFA Level I
#1

P=0.4, RB=0.5 P=0.6, RB=0 RB stands for return of stock B P is the probability associated with it. 1. What is the standard deviation of stock B? this SD seems different from the SD in reading 7 STAT. 2. How to use BAIIplus STAT function to do the calculation?

#2

Variance can be expressed as : Var = E(RB^2) - E(RB)^2 where E(RB) is the expectation value of the return of stock B (ie, the mean), and E(RB^2) is the expectation value of the return of stock be squared. Ie, the mean of the square (NOT the square of the mean). Expectation value of any variable X is the sum over all values X can take of that particular value of X times the probability of finding X in that particular value. In our case there are only two cases, one with probability 0.4 and one with probability 0.6, so we can find the two expectation values as follows: E(RB) = 0.4 * 0.5 + 0.6 * 0 = 0.2 E(RB^2) = 0.4 * (0.5^2) + 0.6 * (0^2) = 0.1 Therefore the Variance is Var = 0.1 - 0.2^2 = 0.06 Standard Deviation is square root of variance, so one gets StdDev = 0.245 I’ve never used the BAII plus, so I wouldn’t know how to use the statistics functions on that, but this is a simple enough problem to just multiply and add and take the square root manually.

#3

Another way: Var = .4 * (.5-.2)^2 + .6 (0-.2)^2 = .4*.09 + .6*.04 = .036+.024 = .06 sd = sqrt(…06) = .245 I am not sure if this can be solved with the BA II Plus calc. CP

#4

cpk’s answer looked a bit easier for me. but i guess mathematically you were talking about the same equation. 3x to both of you.

#5

Here is another method via the BA II Plus… Based on: P=0.4, RB=0.5 P=0.6, RB=0 think of a return of .5 occuring 4 times and a return of 0.0 occuring 6 times. In the [DATA] function enter .5 4 times and 0.0 6 times. The 1 variable [STAT] will display the std. dev.

#6

I feel that it is a moral imperative for me to point out that the above solution, while correct, makes me gag.

#7

Joey, out of curiousity, which of the several solutions above is the one that makes you gag?

#8

Jack’s solution because it is not very general. In particular, if p = 0.162875439, it’s going to take jack a long time to do this problem on his BA II (but Jack seems to know the other way too).