Two Stocks A And B Have A Covariance Of 23 ✓ Solved

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Two stocks (A and B) have a covariance of 23. When combined

Question 1

a) Variance of Stock A and the variance of Stock B.

b) The correlation of Stock A with Stock B.

c) Is portfolio Y efficient? Explain.

d) What is the expected return of portfolio Y?

e) Without doing any calculations, is portfolio X efficient? Explain.

f) What are the characteristics of an efficient portfolio? List at least 3 or 4.

Question 2

a) Your portfolio contains 60% of Bond I and 40% of Bond II. Find the price of Bond II. Find the convexity of Bond I.

Question 3

a) Contrast the concepts of systematic risk and firm-specific risk and give examples of each type of risk.

b) Critique the client suggestion. Discuss what factors are most important in selecting stocks for a portfolio.

Paper For Above Instructions

Introduction

In this paper, we will examine various aspects of portfolio management and risk assessment based on the provided questions. We will analyze the characteristics and performance of financial assets, specifically two stocks with defined covariance, as well as other investment instruments such as bonds. Furthermore, we will delve into modern portfolio theory and the implications of systematic and firm-specific risks.

Question 1 Analysis

To begin with, we need to determine the variances of Stocks A and B given that the covariance between them is 23 and portfolio Y has a variance of 30.25. It is stated that the variance of Stock A is twice that of Stock B. We will denote the variance of Stock B as σ²B and that of Stock A as σ²A. Therefore, we can express σ²A as:

σ²A = 2 * σ²B

When combining the two stocks in equal proportions, the variance of the portfolio (σ²Y) is given by the formula:

σ²Y = (1/2)² σ²A + (1/2)² σ²B + Cov(A, B)

Substituting the values:

30.25 = (1/4) σ²A + (1/4) σ²B + 23

Next, substituting σ²A into the equation:

30.25 = (1/4)(2 σ²B) + (1/4) σ²B + 23

30.25 = (1/2) σ²B + (1/4) σ²B + 23

Combining the terms gives us:

30.25 = (3/4) * σ²B + 23

Solving for σ²B leads to:

σ²B = (30.25 - 23) * (4/3) = 9.67

This implies that Stock A with a variance that is twice that of Stock B has:

σ²A = 19.34.

Next, we can calculate the correlation of Stocks A and B. The correlation (ρ) is defined by the formula:

ρ(A, B) = Cov(A, B) / (σA * σB)

We know Cov(A, B) = 23, and substituting σA and σB, we can determine ρ(A, B).

Next, we need to assess the efficiency of portfolio Y. A portfolio is deemed efficient if no better expected return can be achieved for a given level of risk. With the expected return on the market at 15% and the risk-free rate at 7%, along with the computed standard deviation of portfolio Y, we can compare its Sharpe ratio against existing portfolios.

In regards to portfolio X, to determine if it's efficient without calculations, we would assess its expected return of 17% and compare how this aligns against the established efficient frontier. The characteristics defining an efficient portfolio include maximization of returns at a given risk level, diversification to mitigate indivisible risk, and the balance of systematic vs. unsystematic risk.

Question 2 Analysis

Under the context of bond valuation, your portfolio is composed of 60% Bond I (government bond) and 40% Bond II (corporate bond). Bond I's current price is given as $613.91 for a par value of $1000, indicating a yield can be computed from these figures. For Bond II, with a 2% default premium, its price can be derived based on the expected yield compensation for risk compared to the risk-free rate. Effectively, this would align the pricing mechanisms for both bonds.

Convexity is a measure of the sensitivity of the duration of a bond to changes in interest rates, which can be calculated based on the bond's cash flows and current price. The formula encompasses the present value of cash flows discounted at the bond's yield and offers insight into the bond's price volatility.

Question 3 Discussion

In the realm of portfolio management, differentiating between systematic risk (market risk) and firm-specific risk (unique risk) becomes paramount. Systematic risk affects the entire market and cannot be mitigated through diversification. For instance, economic downturns impact all firms, unlike a company-specific event such as management failure that only influences some stocks. By advising the client to concentrate on five stocks, we may overlook diversified risk management that protects against volatility. Factors such as stock beta, correlation with market movements, and fundamental financial health of firms play crucial roles in determining suitable stock selections for a well-rounded portfolio.

Conclusion

Through this examination of assets, portfolio configurations, and risk characteristics, we highlight fundamental principles in asset pricing and modern portfolio theory. The outcomes not only clarify the financial calculations but also evoke deeper understandings of the strategic applications within investment portfolios.

References

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