Your Investment Club Has Only Two Stocks In Its Portfolio ✓ Solved

Posted on December 17, 2025

Your Investment Club Has Only Two Stocks In Its Portfolio 35000 I

Analyze the financial implications of a small investment portfolio, including calculating portfolio beta, required rate of return based on beta, expected returns with discrete distributions, and the impact of market changes on stock returns and portfolio risk. The analysis should include calculations of beta, expected returns, standard deviations, and the effects of buying, selling, or reallocating stocks within a diversified portfolio, with explanations grounded in finance theory and relevant models.

Sample Paper For Above instruction

Introduction

Investment portfolios are fundamental to asset management, risk diversification, and overall financial planning. The composition and performance of such portfolios depend heavily on the individual assets' characteristics, including beta, expected returns, and market conditions. This paper examines various aspects of portfolio analysis, including beta calculation, required rate of return, expected returns under discrete distributions, and the effects of market variability on investments. By analyzing a hypothetical portfolio consisting of two stocks with differing betas, alongside broader concepts of risk and return, this paper aims to illuminate the practical applications of financial theories in managing investments effectively.

Portfolio Beta Calculation

Calculating the beta of a portfolio comprising two stocks involves weighing the individual stock betas according to the proportion of total investment allocated in each stock. Given an investment of $35,000 in a stock with a beta of 0.5, and $40,000 in a stock with a beta of 2.5, the total portfolio value sums to $75,000. The weight of each stock is determined by dividing the investment in each stock by the total portfolio value. The portfolio beta ($ \beta_{portfolio} $) is then calculated as the sum of the products of each stock’s beta and its weight.Let's perform the calculation:

Weight of Stock 1 ($w_1$) = $35,000 / $75,000 = 0.4667

Weight of Stock 2 ($w_2$) = $40,000 / $75,000 = 0.5333

$ \beta_{portfolio} = (w_1 \times \beta_1) + (w_2 \times \beta_2) $

$ \beta_{portfolio} = (0.4667 \times 0.5) + (0.5333 \times 2.5) = 0.2333 + 1.3333 = 1.5666 $

Thus, the portfolio’s beta is approximately 1.57, indicating the portfolio's sensitivity relative to the market.

Required Rate of Return Calculation

Using the Capital Asset Pricing Model (CAPM), the required rate of return (RRR) on a stock can be computed as:

RRR = Risk-Free Rate + (Beta × Market Risk Premium)

Given the risk-free rate ($r_f$) of 5.5% and a market risk premium of 4%, the calculations for different betas are:

For Beta = 0.8:

RRR = 5.5% + (0.8 × 4%) = 5.5% + 3.2% = 8.7%

For Beta = 2.3:

RRR = 5.5% + (2.3 × 4%) = 5.5% + 9.2% = 14.7%

The required return on the market, calculated as the risk-free rate plus the market risk premium, is 9.5%.

Expected Return and Standard Deviation based on Discrete Distribution

Suppose a stock's return distribution is as follows:

Weak demand (probability $p_1$) with return $r_1$
Below average demand ($p_2$), with return $r_2$
Average demand ($p_3$), with return $r_3$
Above average demand ($p_4$), with return $r_4$
Strong demand ($p_5$), with return $r_5$

Assuming the specific probabilities and returns are given, the expected return ($E[R]$) of the stock is calculated by:

$E[R] = \sum p_i \times r_i$

The standard deviation ($\sigma$) is computed as:

$ \sigma = \sqrt{\sum p_i \times (r_i - E[R])^2} $

This quantifies the volatility based on the probability-weighted deviation of returns from the expected return.

Calculations for Stock Beta and Required Return

Suppose Stock A’s beta is initially 1.0, with known risk-free rate ($r_f$) of 5% and market return ($r_m$) of 10%. The beta indicates the stock's volatility relative to the market. Given the CAPM formula, the required return is:

$ R_A = r_f + \beta_A (r_m - r_f) $

Thus, Stock A’s required return is:

R_A = 5% + (1.0 × (10% - 5%)) = 5% + 5% = 10%

If the beta of Stock A rises to 2.1, the new required return becomes:

R_A = 5% + (2.1 × 5%) = 5% + 10.5% = 15.5%

Impact of Market Conditions on Stock Returns

Given the market required return of 11%, and for stocks with different betas, the changes in market conditions influence the required returns. For Stock X with beta 1.4,:

R_X = 6% + (1.4 × 6%) = 6% + 8.4% = 14.4%

For Stock Y with beta 0.8:

R_Y = 6% + (0.8 × 6%) = 6% + 4.8% = 10.8%

The difference in required returns between the stocks reflects their differing risk premiums associated with market sensitivity.

Portfolio Diversification and Risk Adjustment

Assuming a diversified portfolio of 20 stocks each invested equally at $7,500, with an initial portfolio beta of 1.65, the effect of replacing a stock with beta 1.0 with another stock with beta 0.85 can be assessed by:

New portfolio beta = $ \frac{(W_{old} \times \beta_{old}) + (W_{new} \times \beta_{new})}{Total weight} $

Calculations yield a new beta reflecting decreased overall risk, demonstrating diversification benefits.

Conclusion

This comprehensive analysis underscores the importance of understanding individual asset characteristics, portfolio composition, and market dynamics. Accurate beta calculations enable investors to gauge systematic risk, which directly informs required return estimates via CAPM. Discrete return distributions reveal the potential variability in returns, guiding risk management strategies. Adjustments in portfolio holdings, such as substituting stocks with different betas, significantly impact overall risk and return. Ultimately, adept application of these concepts facilitates informed investment decisions aligned with risk tolerance and financial objectives.

References

Bodie, Z., Kane, A., & Marcus, A. J. (2014). Investments (10th ed.). McGraw-Hill Education.
Fama, E. F., & French, K. R. (2004). The Capital Asset Pricing Model: Theory and Evidence. Journal of Economic Perspectives, 18(3), 25-46.
Damodaran, A. (2012). Investment valuation: Tools and techniques for determining the value of any asset. John Wiley & Sons.
Ross, S. A., Westerfield, R. W., & Jaffe, J. (2013). Corporate Finance (10th ed.). McGraw-Hill Education.
Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77–91.
Lintner, J. (1965). The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets. The Review of Economics and Statistics, 47(1), 13–37.
Sharpe, W. F. (1964). Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk. The Journal of Finance, 19(3), 425–442.
Ameriks, J., & Zeldes, S. P. (2004). How Do Households Respond to Expected Changes in Social Security Wealth? Journal of Public Economics, 88(1-2), 221-249.
Watson, D. G., & Head, A. (2010). Financial Management: Principles and Applications. Cengage Learning.
Elton, E. J., & Gruber, M. J. (1995). Modern Portfolio Theory and Investment Analysis. John Wiley & Sons.

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