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Risk and Return Trade-Off in Portfolios

The golden rule of finance: There is no free lunch. If you want higher returns, you must accept higher risk.

Measuring Return

Expected Return of a portfolio is the weighted average of individual asset returns.

E(R_portfolio) = w1 * R1 + w2 * R2 + ... + wn * Rn

Where:

  • w1, w2, ... = Weights (% invested in each asset)
  • R1, R2, ... = Expected return of each asset

Example:

  • 50% in Stock A (Expected Return = 12%)
  • 50% in Stock B (Expected Return = 8%)
  • Portfolio Return = 0.5 × 12% + 0.5 × 8% = 10%

Measuring Risk

Risk is measured by Variance or Standard Deviation (volatility).

For a portfolio, it's NOT just the weighted average of individual variances. It also depends on Covariance (how assets move together).

Portfolio Variance = w1^2 * σ1^2 + w2^2 * σ2^2 + 2 * w1 * w2 * Cov(R1, R2)
Note

Key Insight: The third term 2 × w1 × w2 × Cov(R1, R2) is the diversification benefit. If Covariance is negative, portfolio risk is LESS than the weighted average of individual risks.

The Trade-Off

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Risk-Free Rate

The Risk-Free Rate is the return you get with zero risk (e.g., Government Treasury Bills). In India, it's around 6-7%.

Any investment with risk should offer a return above the risk-free rate. The extra return is called the Risk Premium.

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