Quantitative Methods - Quantitative Methods Section 2

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46. The covariance matrix for a portfolio is given below.

Security A B
480140
B 140600

  • Option : A
  • Explanation : Standard Deviation of A = √480= 21.91 Standard Deviation of B = √600 = 24.49 Corelation = 0.26
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47. A portfolio manager had invested a total amount of $300,000 in stocks and fixed income instruments at the start of the year. Equity investments represented 60% of the portfolio and generated year-end return of 35%, whereas the fixed income instruments yielded 15%. The correlation of stock returns with fixed income instruments’ returns was found to be 20%. Based on the given data, the portfolio return would be closest to:

  • Option : C
  • Explanation : The total portfolio return is calculated as the weighted average return of the portfolio constituents. Portfolio return = (0.6 * 0.35) + (0.4 * 0.15) = 0.27 = 27.0%
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48. The table below shows information on two portfolios:

 Fund A Fund B
Portfolio weights (%) 4555
Expected returns (%) 1418
Standard deviations (%)  2532
Correlation between the
returns of Fund A and Fund B
0.85 

  • Option : B
  • Explanation : Calculate the portfolio standard deviation of returns as follows:
    Simply Easy Learning
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49. The table below shows weighting and returns of different asset classes comprising a portfolio:

Asset class Asset allocation (weight) (%)Asset class return (%)Correlation with equities class (%)
Equities  6522100
Bonds 308 30
Cash and equivalents 5125

  • Option : B
  • Explanation : The portfolio return is the weighted mean return and is calculated as:0.65 * 22 + 0.30 * 8 + 0.05 * 1 = 16.75.
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50. Arvind Roy currently has two stocks in his portfolio. 30% is invested in Gala Cement and the remainder is invested in Aqua Fertilizer. The two stocks have been performing quite well over the years with expected returns and standard deviations as follows:

Company Expected ReturnStandard Deviation
Gala Cement  10%8%
Aqua Fertilizer  17%20%

  • Option : B
  • Explanation : Systematic risk cannot be reduced.
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