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Portfolio Management
Grenoble Ecole de Management
MSc Finance
2011
2
Rate of return: examples
• Example 1: rate of return
An initial investment is made of EUR 100. One period later the value of the investment
has risen to EUR 125. The rate of return of this investment is:
• Example 2: total rate of return
An initial investment is made of EUR 100. One period later the value of the investment
has risen to EUR 125. In the interim the investor has received an income of EUR 9.
The total rate of return of this investment is:
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Rate of return: examples
• Example 3: real rate of return
An initial investment is made of EUR 100. One period later the value of the investment has
risen to EUR 125. In the interim the investor has received an income of EUR 9 while prices
have grown at a rate of 6%. The total real rate of return of this investment is:
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Rate of return: examples
• Example 4: one-year real rate of return
An initial investment is made of EUR 100. One period later (the period of investment is 3
years) the value of the investment has risen to EUR 125. In the interim the investor has
received an income of EUR 9 while prices have grown at a rate of 6%. The one year total
real rate of return of this investment is:
This return has been realized over 3 years or 36 months, the one-month total
real rate of return of this investment is:
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Rate of return: geometric mean
Given several one-period rates of return, how to calculate
the one-period mean return ?
Example 5: average rate of return
A 3-year investment has registered the following one-year total returns:
5% in year 1, 8% in year 2 and 2% in year 3. The average total rate of
return of this investment is:
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Risk is not a vague concept
Example 6:A 3-year investment has registered the following one-year total
returns: 5% in year 1, 8% in year 2 and 2% in year 3. The variance and
standard error are respectively:
The mean deviation from the mean is 3%. On average, the outcomes of
this investment were distant by 3% of the mean. You can estimate the
variability of any stock or bond returns by the procedure just described.
Portfolio Management
Diversification
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Covariance as a measure of
diversification
Example 7:A 3-year investment in company AA has registered the following
one-year total returns: 5% in year 1, 8% in year 2 and 2% in year 3. A 3-year
investment in company BB has registered the following one-year total
returns: 3% in year 1, -1% in year 2 and 6% in year 3. What is the risk of a
portfolio composed of 50% of AA stocks and 50% of BB stocks ?
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Beta as a marginal risk
Example 8: A 3-year investment in company AA has registered the
following one-year total returns: 5% in year 1, 8% in year 2 and 2% in year
3. A 3-year investment in company BB has registered the following oneyear total returns: 3% in year 1, -1% in year 2 and 6% in year 3. What is the
risk of a portfolio composed of 50% of AA stocks and 50% of BB stocks ?
During the period, the market portfolio has registered the following
returns: 4%, 5% and 3%. What is the Beta of the 50% AA / 50% BB stock to
the market portfolio. What is the marginal contribution of stock AA to the
50%/50% portfolio ?