Treynor Black Model

I don’t know how I’m going to summarize this absolute piece of shit here, but I’ll try:

It represents a portfolio management theory that assumes security markets are nearly efficient. The essence of the model:

1. Security analysts analyze a small number of securities in depth to discover any mispricing. all other securities that are not analyzed are assumed to be fair priced.

2. The Market Index portfolio is the passive portfolio (and lies on the CML), and the expected rate of return and the variance will be provided by the macro forecasting unit of the investment management firm.

3. The objective here is to form an active portfolio with limited securities that are supposedly mispriced.

Now, let’s get on with the steps of this model:

1. First of all, we need to know the beta, and the residual standard deviation of each stock that’s being analyzed. Using CAPM, calculate the RRR for each stock.

2. Next, we calculate the expected return of each stock and the expected abnormal return (alpha) is then calculated by subtracting the RRR from the Expected Return. The cost of less than full diversification comes from the nonsystematic risk of the mispriced stock, th variance of the stock’s residual ( variance of the error term e), which offsets the benefit (alpha) of specializing in an underpriced security.

3. After we’re done calculating the alpha and the residual variance (unsystematic risk) for each stock, we need to calculate the weights of the individual stock that should go to make the active portfolio. The weight of each stock is the alpha value divided by the variance of the residual risk.

4. Next, we calculate the alpha value of the active portfolio by adding up (alpha for each stock)(individual weight from #3). In the same way, calculate the Beta (and the residual variance) for the active portfolio, which is the weighted average of the beta (and the residual variance) of each individual stock.

5. From the residual variance, calculate the standard deviation of the error term.

6. Next we need to find w0, which is the weight of the active portfolio in the optimal risky portfolio, using a formulae. This needs to be adjusted for the beta of the active portfolio, and the new weight is w*.

So, the weight of the market index in the Optimal Risky Portfolio is (1-w*).

7. This is getting more interesting, eh? To calculate the exact make up of the optimal risky portfolio, we will need to calculate the Beta [weighted average of the betas of the market index (it's beta is 1) and the active port.], the Expected Return [using the Market Model method= alpha of the optimal port. + Beta (Market Risk Premium); Alpha of the Optimal Risky Port. is [W(a)*alpha(a)] and the variance (using Market Model Method= (Beta squared)*(Market Risk Premium squared)+(Market Variance squared)].

8. Next we need to calculate the weight given to the Optimal Risky Portfolio (which is called P and lies on the CAL) and the weight allotted to the Risk Free Rate in the overall Portfolio. For this, we use another equation.

If ‘y’ is the weight of the Optimal Risky Port, then (1-y)= Weight in T Bills.

The weight of individual stocks will be= Y*weight of active port (From #6)*weight of each stock (from #3)

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The prediction of alpha needs to be adjusted depending upon the forecast accuracy of the security analysts. This done by first calculating the correlation between the forecasted alpha and the actual alpha value. Either of them can be the independent variable. Next, square the correlation to get R^2, which is the co-efficient of determination, and is a measure of the % change in the dependent variable that is explained by the % change in the independent variable. The higher the value, the better is the forecast of the security analyst. Then multiply the forecasted alpha with R^2 to get the adjusted Alpha. Then we can use this adjusted alpha to again calculate the weights of the stocks and the optimal risky portfolio.

***

I haven’t covered why Active Portfolio Management is helpful even in Efficient Markets. Please go through pages 467-69 for it. I feel too lazy. Sorry!

Reading 72: The Portfolio Management Process And the IPS

This is a small reading and lots of parts build up on what we learned in Level-I. Here’s a small re-cap:

1. Portfolio Perspective: Investments should be judged in the context of the entire portfolio and not on a stand alone basis.

2. There are 3 steps in the Port. Management Process:

• Planning, which includes- Investment Objectives and Constraints, Formulating the IPS (which includes making the investment strategy- active, passive or semi-active), Perceiving the Capital Market Expectations, and Strategic Asset Allocation.

• Execution- Selection of specific assets for the portfolio, interacts constantly with the feedback step. Tactical Asset Allocation- Responding to changes in the short term capital market expectations rather than to investor circumstances. Transaction costs (both explicit and implicit) need to be taken into account).

• The Feedback Step- Includes Monitoring and Rebalancing and Performance Evaluation.

a. During monitoring, two types of factors are monitored: the investor’s circumstances and the economic and market   input factors. We should manage ongoing exposures to available investment opportunities in order to continually satisfy the client’s current objectives and constraints. When asset price changes occur, however, revisions can be required even without changes in expectations.         b. Performance evaluation-Has three steps- Performance measurement (which can be done through 3 sources- market timing, strategic asset allocation and security selection. Port. management is often done against a benchmark. So, both absolute and relative measurement are important), performance attribution (the source of the port’s performance) and performance appraisal (evaluating if the manager did a good job).  The applicability of the benchmark also should be assessed.

Let’s go over the diff. components of the Planning Step in details-

1. Investment Objectives- Includes both risk and return objective. The investment objectives are specific and measurable. Risk tolerance gives more of a range (below average, above average etc.) and risk objective quantifies the risk tolerance. Risk can be measured by absolute methods such as Variance, Std. Deviation, VaR or by relative methods such as Tracking Error. We need to synthesize both the willingness and the ability of the investor to take on risk.

Return Objective: Specify a return measure such as total nominal return, determine the investor’s stated return desire,  the investor’s RRR, and specify an objective in terms of the return measure in the first step. Although an absolute return objective is sometimes set (eg- 10%), the reality of the markets suggest that a relative return objective may be more plausible.

The investment constraints are limitations on the ability to make use of particular investments. They can be liquidity (need for cash in excess of new contributions), time horizon, tax concerns, legal and regulatory factors and unique circumstances (ethical objectives or social responsibility considerations,health needs, support of dependents, avoidance of nondomestic shares etc.)

2. Investment Policy Statement- Is a written document that governs all investment decisions for the client. It is specific to each client and integrates the needs, preferences and circumstances of that client’s objectives and constraints.

It also involved the making of an investment strategy, which is the manager’s approach to investment analysis and security selection. The strategy can either be passive ( a portfolio indexed to a market index or a buy and hold strategy), active (when the port. holdings differ from the port’s benchmark or comparison port, in order to produce a positive alpha), or the semiactive, risk-controlled active or the enhanced index approach (a port. closely following an index strategy, but adding a targeted amt of value by tilting the asset weights in a direction the manager believes to be profitable).

3. Capital Market Expectations- Long run forecasts of risk and return characteristics for various asset classes that form the basis for choosing portfolios.

4. Creating the Strategic Asset Allocation- The manager combines the IPS and the CME to determine the target asset class weights.

Portfolio Management- Reading 69: Markowitz’s "Market Efficiency”

I started this part around 3-4 days back and got done with Readings 68 and 69. I wanted to do a blog post on Reading 68- which is humongous. I might do it later during another revision. I plan to finish Port. Management by this Saturday and then start with Derivatives.

The following are the main points from this reading:

Key assumptions of the Markowitz theory-

1. No taxes or transaction costs
2. All investors hold the same mean variance portfolio
3. Everyone can borrow or lend at the risk free rate
4. Unlimited short selling at the risk free rate and the proceeds can then be used for a long position.

Main implications-

1. The market port. is efficient and lies on the efficient frontier
2. Linear relationship betn. the expected return and beta.

However, in case assumptions 3 or 4 don’t hold, then the key implications would be-

1. The market port. can be inefficient and lie below the efficient frontier.
2. The linear reln. betn the expected return and beta will not hold.
3. Beta cannot be correctly used for the estimation of risk adjustments
4. The high risk averse investors will have a higher concentration of low risk stocks/portfolios. And the low risk averse investors will be diversified by holding a small proportion of high risk stocks/portfolios.

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Tags: MarkowitzTheory, Portfolio Management