8

Portfolio Problem Set Overview

  • The transcript discusses an exercise related to building a portfolio as part of a problem set.

Purpose of Exercise

  • The exercise aims to calculate variances and expected returns for approximately 300 different portfolio combinations using two assets.

  • The instructor emphasizes that this task is meant to prepare students for handling real-world scenarios better without relying solely on computational tools.

Asset Definitions and Parameters

  • Assets Introduced:

    • Asset A:

    • Weight: 0.88

    • Expected Return: 8% (0.08)

    • Standard Deviation: Not specified but an example was provided.

    • Asset B:

    • Weight considered as complementary to Asset A (e.g., 0.12)

    • Expected Return: 6% (0.06)

    • Standard Deviation: 5% (0.05)

  • Correlation Coefficient:

    • A representative value of 0.2 is used to represent the relationship between the two assets.

Combination of Assets

  • The process involves varying the weights of two assets from shorting one asset (-1) to holding twice the amount of that asset (2), iterating with a step of 0.01.

  • Students are encouraged to use Excel to simplify calculations.

Excel Techniques for Portfolio Calculation

  • Creating Weights:

    • Students learn to use Excel’s drag feature to create a range of weights incrementally.

    • Example: Setting the initial weight for Asset A and dragging down to populate weights for various portfolio combinations.

  • Formulas in Excel:

    • Calculating the complement of weights:

    • Example Formula: =1 - [weight of Asset A]

    • Functionality:

    • When the formula is dragged down, cell references update correctly, automatically adjusting for the weight combinations being calculated.

Portfolio Expectation Calculation

  • Formula Representation:

    • Expected Portfolio Return = (Weight of Asset A) * (Expected Return of Asset A) + (Weight of Asset B) * (Expected Return of Asset B)

    • The process of dragging the formula down provides an efficient way to calculate expected returns across all combinations.

CAPM (Capital Asset Pricing Model) Basics

  • CAPM is introduced as a linear model to express asset return concerning their risks.

  • Base Regression Setup:

    • Y Variable: Return of the asset (excess returns of the asset minus risk-free rate).

    • X Variable: Excess return of the market.

    • Understanding the relation of risk (beta) in the context of expected returns.

Implications of CAPM

  • Discussion on what beta means:

    • A higher beta implies higher risk and hence higher expected returns.

  • Example Portfolio Construction:

    • A portfolio consisting of 25% in Asset A, 25% in Asset B, and 50% in risk-free assets, has beta calculated as a weighted average of all betas in the portfolio.

  • Portfolio beta representation shows how exposures in terms of risks can be calculated simply:

    • Example:

    • Portfolio Beta = 0.25 * Beta(A) + 0.25 * Beta(B) + 0.50 * Beta(Risk-Free)

    • Where Beta(Risk-Free) = 0 (zero covariance with the market).

Assumptions of CAPM

  • Key assumptions of CAPM include:

    1. Rational mean-variance optimizers.

    2. Single-period planning horizon.

    3. Homogeneous expectations regarding asset returns across investors.

    4. Publicly traded assets on accessible exchanges without transaction costs.

    5. Investors can borrow and lend at a common risk-free rate, and can short-sell.

Market Portfolio Assumptions

  • The assumption that the market portfolio includes all tradable assets, each held in proportion to its market capitalization.

  • Acknowledgment that many assets (e.g., private companies) are not tradable.

Limitations of CAPM

  • Challenge with empirical testing of CAPM due to misspecified market portfolios and inability to capture cross-sectional variations effectively.

  • The need for extended models due to CAPM's simplicity and assumptions breaking down under certain conditions (multi-period investing).

  • Introduction to ICAPM (Intertemporal Capital Asset Pricing Model) as an extension to handle multiple periods and changing conditions of risk.

Extensions and New Risk Factors in ICAPM

  • Identification of new risks like:

    • Interest Rate Risk: Correlation of asset returns with interest rate changes.

    • Inflation Risk: Impact of inflation on purchasing power and returns in multiple periods, requiring compensation for exposure.

  • Emphasis that investors need to consider changing conditions when reassessing their portfolios over time.

Final Takeaway on CAPM and ICAPM

  • While CAPM remains foundational in finance for understanding the trade-off between risk and return, ICAPM provides a richer framework for examining the complexities of financial markets and investor behaviors beyond a single period.