1. What is the partfolio nisk of holding 11 positions with identi cal volatility

Question

1. What is the partfolio nisk of holding 11 positions with identi cal volatility (any arbitrary volatility) wath one position being 50% ofthe portfolio and the remaining 10 being 5% each? Assume positions are uncorrelated. There are two approaches to thisproblem The direct approach works ith all 11 positions at once. The indirect approach considers a portfolio of portfolios. The following questions assume there are three risky asset classes in the economy Market Capitalization $ trillion) Volatility 20 15 Beta Asset Small Cap Equity Large Cap Equity Corporate & Govt Bonds 1.9 12 20 0.4 2. What are the weights and beta of the market portfolio?

Explanation / Answer

1)

Portfolio risk is measured by standard deviation, which is also known as volatility. It's the deviation of returns from its mean.

Formula: Standard deviatio = Squared-root of Variace
Variance of a Portfolio = [(Variance of stock A * Weight of Stock A)2 + [(Variance of stock B * Weight of Stock B)2+ (2 x Weight of Stock A x Weight of Stock B x Standard Deviation of Stock A x Standard Deviation of Stock B x Co-Relation coefficient of both stocks)]

Since no infomration related to proportion of each position is given, we assume that every position has equal proportion. So, weihgt of each position in portfolio = 1/11 = 0.090909 or 9.0909%

Also, as the positions are uncorelated, co-relation coefficient of the positions will be 0.

Variance of position with 50% volatility = 0.502 = 0.25
Variance of all other positions = 0.052 = 0.0025

Variance of portfolio = (0.090909 x 0.25)2 + (0.0090909 x 0.0025)2 + (0.0090909 x 0.0025)2 + (0.0090909 x 0.0025)2 + (0.0090909 x 0.0025)2 + (0.0090909 x 0.0025)2 + (0.0090909 x 0.0025)2 + (0.0090909 x 0.0025)2 + (0.0090909 x 0.0025)2+ (0.0090909 x 0.0025)2+ (0.0090909 x 0.0025)2 = 0.000517

Portfolio Risk = (0.000517)0.5 = 0.022739

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

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