Lecture 28: R&R2



Investment Analysis: Returns and Risk – Part 2Introduction: Lecture by David Zynda covers calculating expected rates of return and associated risks.Expected Return:

  • Risk: Uncertainty in future investment outcomes (market, credit, operational, liquidity risks).


  • Expected Return Formula:[ E(R) = \sum_{i=1}^{N} (Probability \times Possible Return) ]

  • Historical Returns: Important for setting future expectations using performance indicators.

Example Calculation:

  • 45% chance of recession (-15% return) and 55% chance of expansion (10% return) results in an expected return of -1.25%.

Risk-Free Investment:

  • Represented by US Treasury Bills, offering a certain 5% return.

Economic Conditions:

  • Scenarios:

    • Strong Economy (15%, 20% return)

    • Weak Economy (15%, -20% return)

    • Stable Economy (70%, 10% return)

Expected return calculated as 7%.

Variance & Standard Deviation:

  • Variance measures the volatility around expected returns.


  • Formula:[ \sigma^2 = \sum_{i=1}^{N} (Probability \times (Possible Return - Expected Return)^2) ]

  • Standard deviation is the square root of variance, offering a quick risk assessment.


  • Coefficient of Variation (CV) helps compare risk per unit of return:[ CV = \frac{Standard Deviation}{Expected Return} ]

Historical Returns Analysis:


  • Population variance uses historical returns for clarity:[ \sigma^2 = \sum_{i=1}^{n} (HPY_i - E(HPY))^2 \times \frac{1}{n} ]

  • Excel techniques facilitate calculations and data visualization, aiding risk evaluation.

Practical Application:

  • A final analysis of two stocks illustrated how CV assists in better risk-return trade-offs.