Portfolio Management and Investment Strategies

Posted on Sep 6, 2024 in Economy

Week 1: Portfolio Management and Investment Basics

Portfolio Management Steps:

  1. Evaluate client characteristics
  2. Assess market opportunities
  3. Define objectives and constraints
  4. Set overall investment strategy, including asset allocation
  5. Select investment managers and investment vehicles
  6. Implement strategy
  7. Measure and evaluate performance
  8. Monitor and adjust

Investment Policy vs. Strategy

Investment policy = long term, investment strategy = short term

Investment Objectives

  1. Stability of principal
  2. Income
  3. Growth of income
  4. Capital appreciation

Covariance and Correlation

Covariance is convenient for calculating risk while correlation allows comparisons to be made across different variables. Over time, correlations between markets have been increasing. Diversification only works if correlation is <1 and works better the lower it is.

Week 2: Continuously Compounded Returns

Continuously compounded return is normally distributed. In words: the log of the Expected Gross Return = Expected Continuously Compounded Return + Volatility Adjustment. In general: for single-period problems, it’s easiest to work with gross/discrete returns. For multi-period problems, use continuously compounded returns.

Week 3: Variance of Expected Return and Factor Models

The variance of our expected return estimate depends entirely on the sample length T, not the observation frequency. The single-factor model is an equilibrium model to explain cross-sectional variation in expected return. Factor models are commonly used to describe a simplifying assumption about the structure of correlations amongst assets.

Week 4: Market Efficiency and Noise Trading

Noise makes financial markets possible but also makes them imperfect; if there is no noise trading, there will be very little trade in individual assets. There cannot be full efficiency if the acquisition of information is costly and there are no expected profits from such activity. Then, no one will incur the costs of information-gathering. If no one gathers information, then markets cannot be fully informationally efficient. There is no full information equilibrium.

The Joint Hypothesis Problem refers to the fact that testing for market efficiency is problematic, or even impossible. Any attempts to test for market (in)efficiency must involve asset pricing models so that there are expected returns to compare to real returns. It is not possible to measure ‘abnormal’ returns without expected returns predicted by pricing models. Therefore, anomalous market returns may reflect market inefficiency, an inaccurate asset pricing model, or both. In sum, the joint hypothesis problem implies that market efficiency per se is not testable.

Week 5: Active and Passive Management

Passive Management

Usually characterized by:

  • Index tracking over time
  • Matching market performance
  • Long term buy and hold
  • Manager is assessed in terms of ability to track the target index

Active Management Strategies

Seek to beat a passive benchmark in risk-adjusted terms. Successful active management is usually measured in terms of alpha.

Passive Strategies

  • Full replication
  • Sampling
  • Quadratic optimization

Active Strategies

  • Fundamental analysis: top-down and bottom-up
  • Technical analysis: contrarian and continuation
  • Anomalies and attributes: calendar effect, information effect, security characteristic, investment style

Week 6: Markowitz Model and Black-Litterman Model

Challenges of Using the Markowitz Model

  1. Key parameters are measured with a large degree of sampling error.
  2. Mean-variance optimizers often yield extreme solutions.
  3. The solutions are often very sensitive to slight changes in parameter estimates.
  4. Empirical evidence suggests that it is very difficult to systematically beat benchmark portfolios.

Black-Litterman Model

Idea: Without special/superior information, the market portfolio is optimal and balanced investment. Portfolio holding should only depart from the market portfolio if the portfolio manager’s estimates of expected return on one or more assets differ from the market-implied expected returns.

Steps:

  1. Infer market equilibrium returns for all assets.
  2. Combine equilibrium returns with the manager’s views to arrive at the final estimates of the expected returns of each asset.
  3. Use the final estimates in a Markowitz model to obtain the optimal portfolio.

Instead of solving for a set of weights using the covariance matrix and a set of expected return premiums, we take the weights and covariances to solve for the set of expected returns.

Types of Views:

  • Absolute view: e.g., asset I return = 15%
  • Relative view: e.g., Asset A will outperform asset B by 5%

Advantages of Black-Litterman:

  • Markowitz model requires specifying a full set of expected returns.
  • Using sample means often results in an unbalanced portfolio.
  • Black-Litterman suggests using equilibrium returns that correspond to the balanced market portfolio.
  • Active views can be combined with equilibrium returns to provide better estimates of asset expected returns.
  • Resulted portfolios are balanced and diversified portfolios.

Week 7: Measuring Equity Portfolio Performance

Techniques for Measuring Equity Portfolio Performance:

  1. Composite measures:
    • Treynor ratio
    • Sharpe ratio
    • Jensen measure
    • Information ratio
    • Sortino measure
  2. Holdings-based measures:
    • Grinblatt-Titman measure
    • Characteristic Selectivity measure
  3. Attribution analysis
  4. Stutzer Portfolio Performance Index

Limitations of Attribution Analysis

Attribution analysis can’t be used to assess market timing skills for at least two reasons:

  1. The investment weights are changing throughout the investment period.
  2. TAA involves investment in passive or indexed benchmarks rather than security selection.

Instead, regression analysis can be used.

Stutzer Portfolio Performance Index

It is very hard to define risk aversion. The basic idea is that benchmark underperformance is the risk of foremost concern to managers of active funds. Stutzer suggests a metric that evaluates a portfolio’s performance relative to that of a benchmark in terms of the probability of its outperforming a benchmark. It can be used as the basis of an alternative approach to constructing optimal portfolios that does not depend on estimates of risk aversion and that does not rely on unrealistic assumptions.

Week 8: Stutzer Index and Other Portfolio Optimization Approaches

Stutzer Index

Basic idea: Investors tend to associate risk in investing in active funds with the failure to achieve a benchmark return. Stutzer (2000) proposes a framework to minimize the probability of underperforming a benchmark.

Advantages:

  • Does not assume normal distribution and reflects a preference for positive skewness.
  • The economic objective is to minimize the probability of falling short of a long-run investment target.

Considerations:

  • Highly correlated asset returns will result in an extreme portfolio as in the Markowitz model.
  • Need to ensure that the portfolio has a positive expected excess return over the benchmark. Can use t-tests.

Comparison with Black-Litterman

Both Black-Litterman and Stutzer’s approaches can be viewed as responses to the shortcomings of Markowitz-style portfolio theory, albeit very different.

Other Approaches to Deal with Uncertainty in Estimating Expected Return:

  1. Equal weighting: wi = 1/N, i = 1, …, N
  2. Minimum variance: Invest in Global Minimum Variance Portfolio
  3. Maximum diversification
  4. Risk parity

Week 10: Bond Valuation and Duration

At a higher interest rate, the present value of the payments to the bondholder is lower, so the bond price falls as market interest rates rise. Bond price is convex in interest rate, which means that the price gain when interest rates fall by 1% is larger than the price decline when interest rates increase by 1%. Bonds with greater convexity gain more in price when yields fall and lose less in price when yields increase. If interest rates are volatile, convexity helps to increase the expected return on the bond. Investors are willing to pay higher prices and accept lower yields to maturity on bonds with greater convexity.

The longer the maturity of the bond, the greater the sensitivity of the price to changes in interest rates. Higher coupon issues show smaller percentage price fluctuations for a given change in yield; thus, bond price sensitivity is inversely related to the coupon rate.

Yield to Maturity (YTM)

Yield to maturity (YTM) is the interest rate that makes the present value of a bond’s payments equal to its price. YTM provides a measure of the average rate of return that will be earned on a bond if it is bought now and held to maturity.

Reinvestment Risk

The realized rate of return of the bond over its life is only equal to YTM if all coupons are reinvested at an interest rate equal to the bond’s YTM. When the interest rate changes over time, the realized compound return will not be equal to YTM. Interest rate changes lead to reinvestment risk for bondholders.

Bond Price Risk

Interest rate changes lead to changes in bond prices and create bond price risk. Bond prices change in the opposite direction of the reinvested coupon income as the interest rate changes. An increase in the interest rate will increase reinvested coupon income but result in a capital loss in the form of a reduced bond price.

Duration Analysis

Duration analysis assumes a flat yield curve, which means the bond’s YTM is the same as the interest rate.

Passive Bond Strategies

  • Immunization: Hedge against interest rate risk
  • Indexing strategy: Replicates the performance of a given bond index

Active Bond Strategies

  • Substitution swap
  • Intermarket spread swap
  • Rate anticipation swap
  • Pure yield pickup swap

Limitations of Immunization and Duration Analysis

Immunization and duration analysis are based on the assumption that market interest rates are expected to remain at a constant level for a long time period. In other words, it assumes a flat yield curve, and all payments are discounted at a common interest rate. Under this assumption, interest rate changes always involve a parallel shift of the yield curve. In practice, when yields change, the yield curve seldom experiences a parallel shift. When the yield curve experiences a nonparallel shift, these methods provide imprecise estimates.

Week 11: Stock Index Futures and Swaps

Stock Index Futures

  • Allow investors to hold the market portfolio without having to buy or sell a large number of stocks.
  • Used by market timers to speculate on broad market movements.
  • Market timers shift between Treasury bills and stock index futures. They are long in many futures contracts and T-bills when bullish and hold only T-bills when bearish.

Arbitrage

Arbitrage can sometimes be created through fast trading. SuperDOT is a program to do that.

Hedging with Futures

Once market risk is hedged, the performance of the stock plus futures contract portfolio will depend only on the firm-specific performance of the stock.

Cross Hedging

Future and spot price changes are usually proportional in theory, however, in practice, yields can vary considerably across sectors, and the hedge is in fact a cross hedge. Nevertheless, even cross hedges can eliminate a large fraction of the total risk of the unprotected portfolio.

Swaps

A swap obligates two counterparties to exchange cash flows at one or more future dates. Foreign exchange swaps enable firms to quickly and cheaply restructure their balance sheets. The interest rate parity can be used to determine the arbitrage-free forward rate for each period.

Week 12: Quantitative Analysis and Event Studies

Quantitative analysis looks at event studies.

Defining Event Windows

◦ Analysing the statistical properties of excess returns in each of these three windows tells us: Estimation window: If the market had prior knowledge of the announcements Event window: How much the market actually reacted to the event Post-event window: How much post announcement drift there was