Corporate Finance: Risk-Free Assets and Portfolio Variance

This corporate finance assignment delves into the impact of diversification and the addition of new shares on portfolio risk and return. It explains the concepts of systematic and unsystematic risk, highlighting how diversification can minimize unsystematic risk. The assignment emphasizes the importance of correlation coefficients between new shares and the existing portfolio, with negative correlations leading to higher risk reduction. It further analyzes the effect of incorporating a risk-free asset into a portfolio, demonstrating how the portfolio variance simplifies to a function of the weight and risk of the risky asset. The solution references key texts in corporate finance to support its analysis. Desklib provides access to this and other solved assignments for students' learning needs.

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Question 2
The diversification concept forms the basis of outlining the impact of a new stock in the
portfolio. Diversification is considered beneficial as there are two kinds of risk associated
with investing in risky financial asset classes. One of these is the systematic risk while the
other is unsystematic risk. If the investors form a well-diversified portfolio, they can
minimise the unsystematic risk but the systematic risk would remain. Considering that
formation of a diversified portfolio leads to potential minimisation of unsystematic risk,
hence to that extent addition of a new share would reduce the overall portfolio risk. (Petty et.
al., 2015).
However, the precise impact of addition of new stock on risk reduction would be dependent
on the correlation between the returns of the new share with the existing portfolio. A negative
correlation in this regards is favourable since it would lead to higher risk reduction as
highlighted in the following formula for portfolio risk for a two stock portfolio (Damodaran,
2015).
P1,2 denotes the correlation coefficient in the above formula and it is not hard to see that if this
is negative, there would be a net reduction in the portfolio risk. This can also be understood
by mirroring the respective movements of the two stocks. Stocks having negative correlation
coefficient on their returns would tend to move in opposite direction and hence extreme
variations from mean would be curtailed owing to a natural hedge mechanism in place
(Parrino & Kidwell, 2014). It would be imprudent to conclude that risk would not be reduced
in case of positive correlation. Risk reduction would be exhibited in stocks having positive
correlation between returns but the extent is lesser. However, a key advantage of portfolio

CORPORATE FINANCE
formation with risky assets is that portfolio invariably tends to lead to a higher returns per
unit risk assumed and hence becomes preferred over individual stocks (Brealey, Myers. &
Allen, 2014).
.Question 3
The given formula for variance in case of a portfolio comprising two assets is indicated as
follows.
In the given portfolio, it is learnt that a risk free asset is present. As the name suggests, a risk
free asset would have zero risk and as variance tends to act as indicator of risk, hence
variance associated with such a asset would be zero. Also, the correlation coefficient between
the returns of the risk free asset and risky asset would be zero (Petty et. al., 2015).
Based on the given inputs, the portfolio variance is summarised below.
σp2 = w12*02 + w22*σ22 + 2w1w2*0*σ2*0
All the terms on the right hand would be zero barring the middle term which would remain.
Hence, the simplified version of two asset portfolio variance is presented below.
σp = w2σ2
From the above result, it is apparent that portfolio risk in this case would be function of the
weight of risky asset and the underlying risk associated with such asset (Damodaran, 2015).

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References
Brealey, R. A., Myers, S. C. & Allen, F. (2014) Principles of corporate finance, 6th ed. New
York: McGraw-Hill Publications
Damodaran, A. (2015). Applied corporate finance: A user’s manual 3rd ed. New York:
Wiley, John & Sons.
Parrino, R. & Kidwell, D. (2014) Fundamentals of Corporate Finance, 3rd ed. London:
Wiley Publications
Petty, J.W., Titman, S., Keown, A., Martin, J.D., Martin, P., Burrow, M. & Nguyen, H. (2015).
Financial Management, Principles and Applications, 6th ed.. NSW: Pearson Education,
French Forest Australia