Portfolio ManagementGrenoble Ecole de ManagementMSc Finance2011

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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 conceptExample 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.

Diversification

Portfolio Management

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Covariance as a measure of diversificationExample 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 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 ? 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 ?