Lecture 8 Summary

Lecture Overview

  • Topic: Investments and Portfolio Selection

  • Focus Areas: Portfolio Performance Evaluation, Fixed Income Introduction

Key Points

8.1 Portfolio Performance Evaluation

  • Measures of performance

  • Examining if fund managers outperform markets

8.2 Performance Attribution

  • Difference in returns from asset allocation vs. security selection

8.3 Introduction to Fixed Income

  • Characteristics and pricing of bonds

  • Bond price in relation to par value

Performance Measurement

  • Benchmark Model: ( R_{it} = \alpha_{i} + \beta_{i} R_{Mt} + \epsilon_{it} )

  • Distinction between returns from systematic risk (( \beta )) vs. skill in selection (( \alpha )).

  • Adjust for risk when evaluating performance.

Evaluation Metrics

Sharpe Ratio

  • Measures return per unit of total risk

  • Higher Sharpe indicates better risk-adjusted return

M^2 Measure

  • A standardized Sharpe ratio for comparing investments under equalized risk conditions

  • ( M_i^2 = \frac{\sigma_{M}}{\sigma_{i}} (E R_i - E(R_M)) )

Treynor Measure

  • Focuses on systematic risk for well-diversified portfolios

  • ( T_i = \frac{E R_i - r_f}{\beta_i} )

  • Positive alpha implies an asset sits above the SML.

Performance Attribution

  • Returns can be attributed to asset allocation or security selection:
      - Asset Allocation (AA): Variance due to weights across asset classes.
      - Security Selection (SS): Variance from chosen securities within classes.

Bond Pricing Basics

  • Bonds represent debt obligations between issuers and bondholders.

  • Key Parameters:
      - Time to maturity
      - Face value (par value)
      - Coupon rate and frequency
      - Yield to maturity (YTM)

  • Pricing equation incorporates cash flows to bondholders:
      ( P_B = \sum_{t=1}^{T} \frac{C_t}{(1+y)^t} + \frac{FV}{(1+y)^T} )

Discount, Premium, and Par Bonds

  • Discount Bonds: Price < Face Value (CVR < YTM)

  • Premium Bonds: Price > Face Value (CVR > YTM)

  • Par Bonds: Price = Face Value (CVR = YTM)

  • Price inversely related to YTM changes.

Conclusion

  • Evaluating fund manager performance and bond pricing is crucial for informed investment decisions.