MAF101 Lecture Notes - Lecture 6: Standard Deviation, Weighted Arithmetic Mean, Market Risk
14 Jun 2018
School
Department
Course
Professor
MAF101 FUNDAMENTALS OF FINANCE
Kieu Trang Nguyen
Study notes
TOPIC 3 Risk & Return (PART III)- Lecture 6
*THE KEY TO REDUCE PORTFOLIO RISK (FROM LAST WEEK)
• The real advantages of diversification result from the risk reduction caused by combining
securities whose returns are less than perfectly positively correlated.
➢ As long as the correlation coefficient is less than +1, (even at 0.9 or 0.5), there is a
benefit to diversifying through forming a portfolio i.e. σp<w1σ1+w2σ2. The portfolio
standard deviation is less than the weighted average of the two asset’s standard
deviation.
•
The degree of risk reduction increases as the correlation coefficient between the returns
on the two securities decreases.
➢ The largest risk reduction available is where the returns are perfectly negatively
correlated (-1), so the two risky securities can be combined to form a portfolio that has
zero risk, σp=0.
*PORTFOLIO RISK AND RETURN: 3 ASSETS
The expected return of the portfolio is 16.5% p.a
• The standard deviation or risk of the portfolio is 9.85% p.a. The actual calculation of the
standard deviation number is beyond the scope of this unit. However the implications of
this number is important.
• While the portfolio expected return is the weighted average of the individual asset
expected returns, the portfolio standard deviation is lower than weighted average of the
individual assets standard deviation and lower than the standard deviation of any of
the assets that make up the portfolio.
• This is the benefit of diversification.
• Source of the diversification benefit: the negative correlation between assets 1 and 3 and
the zero correlation between assets 2 and 3.
*PORTFOLIO RISK AND RETURN
• There are 2 standard deviation terms and 2 correlation terms.
• In a portfolio comprising of 3 assets, there are 3 std. dev. terms and 6 correlation terms.
• If the number of assets in the portfolio is 4, there are 4 std. dev. terms and 12 correlation
terms.
• It can be shown that in a portfolio comprising of many assets ‘m’, the number of std. dev.
terms is m while the number of correlation term is m(m-1).
➢ If m=10, the number of std. dev. terms is 10 while the number of correlation terms is
10(10-1)= 90.
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Document Summary
Topic 3 risk & return (part iii)- lecture 6. *the key to reduce portfolio risk (from last week) securities whose returns are less than perfectly positively correlated. benefit to diversifying through forming a portfolio i. e. p
