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# Safest Portfolio to Invest In Under Restrictions

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Your eccentric Aunt Claudia has left you \$50,000 in Alcan shares plus \$50,000 cash. Unfortunately her will requires that the Alcan stock not be sold for one year and the \$50,000 cash must be entirely invested in one of the stocks shown in Table 7.8. What is the safest attainable portfolio under these restrictions?

Correlation Coefficients
Alcan BP Deutsche Bank KLM LVMH Nestle Sony Standard deviation
Alcan 1 0.39 0.55 0.54 0.61 0.26 0.36 30.20%
BP 1 0.23 0.29 0.22 0.3 0.14 23.90%
Deutsche Bank 1 0.36 0.48 0.16 0.39 38.10%
KLM 1 0.49 0.32 0.19 54.50%
LVMH 1 0.02 0.5 42.00%
Nestle 1 0.1 15.50%
Sony 1 47.50%

Table 7.8

#### Solution Preview

Safest portfolio means that the standard deviation of returns of the portfolio must be minimum
We have to invest \$50,000 in one of the stocks such that the standard deviation of the portfolio is minimum.
Thus, out of a total investment of \$100,000, 50% of the investment (\$50,000) is in Alcan and 50% (\$50,000) is in one of the stocks

Variance (square of standard deviation ) of a portfolio consisting of two stocks is equal to
sp2 = w12* s12 + w2 2* s22 +2w1w2rho12s1s2
where w1, w2 are proportions invested in stock 1 and 2 respectively; here both are equal to ...

\$2.19