3. Probability ideas, including joint probability distributions, play a major ro

Question

3. Probability ideas, including joint probability distributions, play a major role in financial activities. For example, portfolio managers must allocate funds among competing assets. Suppose there are two assets: Microsoft (M) stock and Starbucks (S) stock. For Microsoft stock, the following returns are possible -10%, 10%, 20%, and 30%. For Starbucks stock, the following returns are possible: 0% and 20%. The Joint probability distribution of the returns of the two assets is Microsoft stock (M) 0% 20% -10% 0.05 0.10 10% 0.20 0.15 20% 0.10 0.20 30% 0.05 0.15 Starbucks stock (S) a. What is the expected return on Microsoft stock? b. What is the expected return on Starbucks stock? c. What is the standard deviation (or volatility) of the returns on Microsoft stock? d. What is the standard deviation (or volatility) of the returns on Starbucks stock? e. Are the returns on Microsoft stock and the returns on Starbucks stock statistically independent?

Explanation / Answer

let X is starbucks stock and Y Microsoft :

marginal pdf of starbucks:

and marginal pdf of Microsoft:

a) expected return of Microsoft E(Y)=14

b)expected return of Starbukcs E(X)=12

c)std deviation of Microsoft=SD(Y)=(154)1/2 =12.41

d)std deviation of Starbucks=SD(X)=(96)1/2 =9.80

e)No as P(X=0; Y=-10) =0.05 ; while P(X=0)*P(Y=-10)=0.15*0.4=0.06

as they both are not equal ; stocks are not independent,

x P(x) xP(x) x^2P(x) 0 0.4000 0.0000 0.0000 20 0.6000 12.0000 240.0000 total 1 12 240 E(x) = 12.0000 E(x^2) = 240.0000 Var(x) E(x^2)-(E(x))^2 96.0000

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.