Financial Markets: Valuing Assets and Managing Their Risk Blackwell, Griffiths and Winters

1
Financial MarketsValuing Assets and Managing
Their RiskBlackwell, Griffiths and Winters

• Chapter 14
• Portfolio Formation and
• Risk Management

2
The Basics of Portfolio Formation

• A portfolio is a group of assets. The relative
  importance (weight) of an asset in a portfolio is
  based on the assets contribution to the value of
  the portfolio.
• We will focus on forming a stock portfolio.

3
The Basics of Portfolio Formation (continued)

• Example
• Lets assume we have 15,000 invested in our
  portfolio and the investment is divided among
  three stocks
• FLYBY 5,000 33
• UO 6,000 40
• GDAY 4,000 27

4
The Basics of Portfolio Formation (continued)
Example (continued)
5
The Basics of Portfolio Formation (continued)
Example (continued)
So, what is the likely return on the portfolio?
The answer is the weighted average of the
individual returns.
Also, what is the Beta of the portfolio? The
answer is the weighted average of the individual
Betas.
6
The Basics of Portfolio Formation (continued)
Example (continued)

• The third calculation we would like to do for our
  portfolio is its standard deviation. However,
  the standard deviation of the portfolio is not
  the weighted average of the individual standard
  deviations because of the difference between
  diversifiable and non-diversifiable risk.

7
The Basics of Portfolio Formation
(continued)Correlation

• The degree of correlation is a measure of the
  extent to which returns on two assets move
  together.
• If both move up and down together, they are
  positively correlated and ?ij gt 0.

8
The Basics of Portfolio Formation
(continued)Correlation (continued)

9
The Basics of Portfolio Formation
(continued)Correlation (continued)

• If one moves up when the other moves down, they
  are negatively correlated and ?ij lt 0.

10
The Basics of Portfolio Formation
(continued)Correlation (continued)

• If the two assets are completely independent,
  then they are uncorrelated and ?ij 0.

11
Measuring Portfolio Risk

• We now want to measure portfolio risk and since a
  portfolio has more than one asset we have to
  consider the correlation of the assets in the
  portfolio.
• The standard deviation of a portfolio includes
  the correlation between the assets in the
  portfolio and thus provides a measure of
  portfolio risk.

12
Measuring Portfolio Risk (continued)

• The formula for portfolio standard deviation is

13
Measuring Portfolio Risk (continued)
Now, lets return to our portfolio and calculate
its standard deviation.
The shaded area (on the diagonal) represent the
weighted total risk of the of the individual
securities in the portfolio, which in the
formula is Swi2si2
14
Measuring Portfolio Risk (continued)

• The off-diagonal items represent the correlations
  between the different assets in the portfolio and
  the formula is
• 2(SSwiwj?ijsisj)
• The formula starts by multiplying by 2 because
  the item above the diagonal are the same as the
  times below the diagonal.

15
Measuring Portfolio Risk (continued)
Using our portfolio, the cells of the figure are
as follows
16
Measuring Portfolio Risk (continued)
Now, the calculation for the portfolio standard
deviation is