NISM Series XXI-B — Portfolio Managers

Welcome to NISM Series XXI-B — Portfolio Managers. Follow Modern Portfolio Theory: Diversification, Correlation and the Efficient Frontier, then practise in the learning system. Sign in and use the study header to open your authorised course. Select this published lesson. Start Course Tutor with Auto audio on: it teaches continuously, answers a typed question, then resumes. Risk of a portfolio. Risk is measured by variance or its square root, standard deviation. For a portfolio, the variance depends on each asset's own variance and on the covariance between each pair of assets. Data (invented). Asset A (equity approach): expected return 14%, standard deviation 20%. Asset B (debt approach): expected return 8%, standard deviation 10%. Correlation ρ = 0.2. Weights: 60% in A, 40% in B. Step 1 — expected return. 0.6 times 14 + 0.4 times 8 = 8.4 + 3.2 = 11.6%. Step 2 — variance. wA squared sigma A squared = 0.36 times 400 = 144. wB squared sigma B squared = 0.16 times 100 = 16. Covariance term = 2 times 0.6 times 0.4 times 0.2 times 20 times 10 = 0.48 times 0.2 times 200 = 19.2. sigma p squared = 144 + 16 + 19.2 = 179.2 (in squared percentage units). Step 3 — standard deviation. square root of 179.2 = 13.39% (approximately). Check: square root of 179.2 approximately 13.38656, and 13.38656 squared approximately 179.2; 13.39% is the two-decimal display. Step 4 — the diversification benefit. The weighted-average standard deviation is 0.6 times 20 + 0.4 times 10 = 16%. The portfolio's actual risk is 13.39%, about 2.6 percentage points lower, because the correlation is well below 1. Step 5 — sensitivity to correlation. If ρ = +1: sigma p = 0.6 times 20 + 0.4 times 10 = 16% (no benefit). If ρ = 0: sigma p squared = 144 + 16 = 160; sigma p = 12.65%. If ρ = −1: sigma p = |0.6 times 20 − 0.4 times 10| = |12 − 4| = 8%. Check for ρ = 0: square root of 160 approximately 12.64911; the two-decimal display 12.65 gives 12.65 squared =160.0225 approximately 160.02. The expected return of 11.6% does not change with correlation; only risk does. This is why managers look for assets with low correlation to existing holdings. Step 6 — a CML reading. Suppose (invented) the market portfolio has expected return 12% and standard deviation 16%, and the risk-free rate is 6%. The CML slope is (12 − 6) divided by 16 = 0.375. A client who wants a standard deviation of 8% would hold half in the market portfolio and half in the risk-free asset, with expected return 6 + 0.375 times 8 = 9%. Check: 0.5 times 12 + 0.5 times 6 = 9%. Confirmed. Ask Course Tutor to explain this step: Check: square root of 179.2 approximately 13.38656, and 13.38656 squared approximately 179.2; 13.39% is the two-decimal display. Step 4 — the diversification benefit. Say what you tried. Pause and try this source task. What is the covariance of two assets with standard deviations 20% and 15% and correlation 0.5? The source answer is: 0.5 times 20 times 15 = 150 (squared percentage units). Compare your method and result, correct an error, then continue. Use Stop to end Course Tutor.