Given the following probability distribution, what is the standard deviation of returns for Security J? (Expresss your answer in percentage, but do not include the percent sign, %, i.e., 4.65) State Pi rJ 1 0.2 8 % 2 0.6 12    3 0.2 17

Example 3 Inns oont alafrA Following Example 2, consider a porfolio with three assets S1, S2 and S3 which have expected rates of return 0.1,0.15 and 0.2 respectively, and variance-covariance matrix odni tanoma bszt a aitevi ot botoly 0.1 0.1 -0.1 0.1 0.2 0.1 ololles V = -0.1 0.1 0.6 vo ) isaas sod slais a at gaiteoo ottg ndi oda vodT (aldanoitesup als ot-lais wod ibuadala abnod on a) What is the optimal portfolio when up = worod of sidad = 0.2. adt yhalinie ini ba moe ja SOLUTION lo ano ot b) Use this piece of information and the earlier optimal portfolios from la aao e. Example 2 to find the quadratic equation relating of and up. ni bstni sd SOLUTION tar oad o bo s e) Hence draw a plot of the solutions, and identify the frontier port- Ldon to slar folios. it SOLUTION ods Btvni gatela dt

A coefficient of determination of 0.6 means that \\( 40 \\% \\) of the variation in a security's return is related to factors other than the security's relationship to the market. True False

Prob. Return (%) B 0.1 40 G 0.2 30 O 0.3 15 L 0.2 2 S 0.2 -12 where B-Bloom,G-Good, O-Ok, L-Level and S- Slump   Probability(p(x)) Return(x) (%) x*p(x) x2*p(x) B 0.1 40 0.1*40=4 0.1*402=160 G 0.2 30 0.2*30=6 0.2*302=180 O 0.3 15 0.3*15=4.5 0.3*152=67.5 L 0.2 2 0.2*2=0.4 0.2*22=0.8 S 0.2 -12 0.2*-12=-2.4 0.2*(-12)2=28.8 Expected return==E(x)=∑x*p(x)=4+6+4.5+0.4-2.4 =12.5% Variance of return=E(x2)-[E(x)]2 E(x2)=∑x2p(x)=160+180+67.5+0.8+28.8 = 437.1 Variance= 437.1-(12.5)2 = 280.85 sd of return= 280.85 = 16.76% The expected return on Granny's gold investment is 12.5% The sd of return on Granny's gold investment is 16.76% 1. In your own words, define the two components of total risk? Give examples of both risks.2. How is beta estimated or calculated?