Situation 1 - Good economy state, probability = 0.7, stock A return = 15%, bond
ID: 2735927 • Letter: S
Question
Situation 1 - Good economy state, probability = 0.7, stock A return = 15%, bond B return = 4%
Situation 2 - Bad economy state, probability = 0.3, stock A return = 6%, bond B return = 8%
Calculate the expected return and standard deviation of return for the portfolio, using scenario analysis method (use portfolio’s return in each state and then follow the definition of E(r) and std.) and the portfolio theory formula (Applying E(r) and std. of A and B and the correlation coefficient between A and B).
1. Definition: ( for every possible scenario) p, x, and var(r)=-- > pil 2. Portfolio situation: (i for every possible scenario) The rate of returns for A and B in every scenario is ria and iB. The expected return and standard deviation of return for A and B are (E(a), .) and (E('s ),Og ) respectively, and WA WB are investment weights on asset A and B, then: a. Relationship between returns of A and B: b. Three rules of portfolio return and risk Rule 1: ,,-WJa +11e's this is for every scenerio Rule 2: E('s)-w,E(.)-ngE('s) +gthis is for Rule 3: +1. +21v,w.cov (r,.r ,,'s) Since Cov(r,,r,) ='W A BPABExplanation / Answer
Stock A:
Expected return = Probability * Expected return of good economy + Probability * Expected return of bad economy
= 0.70*15% + 0.30 * 6%
= 12.3%.
Expected return of stock A = 12.3%.
Stock B.
Expected return = Probability * Expected return of good economy + Probability * Expected return of bad economy
= 0.70*15% + 0.30 * 6%
= 5.2%.
Expected return of stock B = 5.2%.