Chapter 10: NISM-XV Exam Prep
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Day 47: NISM-XV Module 6 — Portfolio Theory
Beta, Sharpe ratio, systematic vs unsystematic risk — the maths behind smart investing
2 min read
📖 Priya's Exam Question
Exam hall. Question 47: "Calculate the expected return of Priya's portfolio given the following weights and expected returns..."
Priya smiled. She'd seen this exact type of question during revision. She wrote the formula, applied it in 90 seconds, moved on.
The exam rewards students who learn the mechanics, not just the concepts. Let's learn both. 📐
Exam hall. Question 47: "Calculate the expected return of Priya's portfolio given the following weights and expected returns..."
Priya smiled. She'd seen this exact type of question during revision. She wrote the formula, applied it in 90 seconds, moved on.
The exam rewards students who learn the mechanics, not just the concepts. Let's learn both. 📐
Systematic vs Unsystematic Risk
| Risk Type | What It Is | Can You Diversify Away? |
|---|---|---|
| Systematic (Market) Risk | Affects entire market — recession, war, interest rate changes | NO — you're stuck with it |
| Unsystematic (Company) Risk | Affects one company or sector — fraud, product failure | YES — by diversifying across stocks! |
Beta — Measuring Market Sensitivity
Beta = How much a stock moves relative to the market (benchmark = 1.0)
β = 1.0 → Moves exactly like the market. Nifty +5% = Stock +5%
β = 1.5 → Moves MORE. Nifty +5% = Stock +7.5% (riskier!)
β = 0.5 → Moves LESS. Nifty +5% = Stock +2.5% (defensive)
β = -1.0 → Moves OPPOSITE to market (rare — some gold stocks)
High Beta: Mid/small caps, infrastructure, metals
Low Beta: FMCG, pharma, utilities — defensive sectors
β = 1.0 → Moves exactly like the market. Nifty +5% = Stock +5%
β = 1.5 → Moves MORE. Nifty +5% = Stock +7.5% (riskier!)
β = 0.5 → Moves LESS. Nifty +5% = Stock +2.5% (defensive)
β = -1.0 → Moves OPPOSITE to market (rare — some gold stocks)
High Beta: Mid/small caps, infrastructure, metals
Low Beta: FMCG, pharma, utilities — defensive sectors
Portfolio Expected Return Calculation
Portfolio Return = Sum of (Weight × Expected Return) for each asset
Priya's Portfolio:
Reliance: 40% weight, expected 15% return
Zomato: 30% weight, expected 25% return
Govt Bond: 30% weight, expected 7% return
Portfolio Return = (0.40×15) + (0.30×25) + (0.30×7)
= 6 + 7.5 + 2.1 = 15.6% expected return!
Priya's Portfolio:
Reliance: 40% weight, expected 15% return
Zomato: 30% weight, expected 25% return
Govt Bond: 30% weight, expected 7% return
Portfolio Return = (0.40×15) + (0.30×25) + (0.30×7)
= 6 + 7.5 + 2.1 = 15.6% expected return!
Sharpe Ratio — Risk-Adjusted Performance
Sharpe Ratio = (Portfolio Return − Risk-Free Rate) / Standard Deviation
Sharpe > 1 = Good. Sharpe > 2 = Very Good. Sharpe > 3 = Exceptional (rare!)
Why it matters: A fund returning 18% with huge volatility may be WORSE than one returning 14% smoothly. Sharpe ratio captures this — compare risk-adjusted returns, not raw returns!
Exam question: "Fund A Sharpe = 1.8, Fund B Sharpe = 1.2 — which is better?" → Fund A, always.
Sharpe > 1 = Good. Sharpe > 2 = Very Good. Sharpe > 3 = Exceptional (rare!)
Why it matters: A fund returning 18% with huge volatility may be WORSE than one returning 14% smoothly. Sharpe ratio captures this — compare risk-adjusted returns, not raw returns!
Exam question: "Fund A Sharpe = 1.8, Fund B Sharpe = 1.2 — which is better?" → Fund A, always.
🎯 Takeaway:
Systematic risk = cannot diversify. Unsystematic risk = can diversify. Beta > 1 = more volatile. Portfolio return = weighted average. Sharpe ratio = risk-adjusted performance — higher is better. Tomorrow: Mutual Fund Regulations!
Systematic risk = cannot diversify. Unsystematic risk = can diversify. Beta > 1 = more volatile. Portfolio return = weighted average. Sharpe ratio = risk-adjusted performance — higher is better. Tomorrow: Mutual Fund Regulations!