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)

****

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 54: Hedge Fund Risks and How to Manage Them

There are three types of hedge fund risks: Investment risks, fraud risks and operational risks.

Investment risks: Risks due to the nature of the markets, manager styles,strategies, securities held and derivatives used. Note that a manager’s style does not necessarily define the risks, as two managers pursuing the same style can have very different strategies and risks..

Limited Information on Hedge Fund Risk- Unfortunately, most data for hedge funds only goes back to as far as the late 1980s or early 1990s. This was a stable period in the hedge fund history and so it is difficult to forecast the future risks.

Credit spreads and fixed income funds- The largest factor here is the widening of credit spreads.

Equity Market Risk and Fixed Income Funds-

Widening credit spreads, declines in the stock market and losses at fixed income hedge funds are correlated to one another. This is because most FI hedge funds are short treasury bonds and long corp. bonds. During eco. slowdown, the credit spread widens, and the loss from the short treasury position creates a net loss, esp. if the bond issuers on the long side are also experiencing a financial difficulty.

Equity Market Risks- As mentioned earlier, even though market neutral funds have zero beta and low volatility, they are affected by the market movements. Long/short equity funds have higher standard deviations and higher correlation compared to either market neutral or risk arbitrage funds.

Emerging market funds actually have a low beta in a bullish market and a high beta in a bearish market. So, they don’t fully participate in a high market and suffer great losses in a down market.

Style drift and Leverage- Managers often take on addl. leverage and drift from their style to take advantage of market movements. However, over the long term, this is not a good tactic because they might lack expertise in the area of the new style.

Fraud Risk:

This represents misrepresentation of background qualifications, assets under management etc. by the manager. If the returns are too go to be true, then they probably are.

Operational Risk:

Arises from deficiency in procedures, infrastructure, resources, supervision or trade data.

There are some other types or risks such as counterparty risk, transaction risk and settlement risk.

Measuring Hedge Fund Risk

There are two methods that can be used=

Maximum Drawdown- Is the % decrease in investment value from its peak to its valley. It is the largest drawdown that has ever occurred within a specific time frame. However, it doesn’t give us the probability of the drawdown.

Value at Risk- Not only does it given an estimate of left tail risk , but also the probability. for example- there is a 99% (3 standard deviation minus) chance that the loss will not be more than 12% of its value over the next quarter.

Limitations of using VaR-

1. Generally uses historical data, which might not be repeated in the future.
2. Uses a normal distribution , whereas hedge fund returns re not normally distributed.
3. Computed assuming that the components are additive, whereas they are multiplicative in real life!

Some other methods:

Loss standard deviation- similar to standard deviation, but focuses on the left tail return.

Downside standard deviation- Measures left tail risk, but gives an acceptable threshold of return.

Sortini Ratio= Somewhat like Sharpe ratio, but it uses the downside deviation instead of standard deviation and the minium acceptable return in place of the risk free rate.

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Tags: HedgeFunds, Equity Valuation, CFA, Finance, Business

Reading 53: Evaluation of the Performance of your Hedge Funds

1. There are generally four types of hedge funds: Long/short funds, Global Macro Funds, Event Driven funds and market neutral funds.

2. Two methods of evaluation performance:

Jensen’s Alpha (ex post alpha): E(R)= Rf+ Beta (Market Risk Premium). Positive alpha means the port. is undervalued and a negative alpha means the port. is over-valued.

The Sharpe Ratio: (Ra-Rf)/Standard Deviation

3. It is difficult to compare a hedge fund to a benchmark due to the following reasons-

• Changes in Leverage- Even though a Fixed income arbitrage hedge fund might use leverage as high as 20 times its capital base, the benchmark index that is used is not multiplied twenty times.

• Changes in Hedging Techniques- Even though a market neutral fund has very low volatility because of the long and short positions that it takes, it is affect by the change in the market index. It maintains its short position either by short selling stock or by purchasing put options and paying the put premium. In case of a down market, short selling is more advantageous, even though the put option caps the loss at the premium paid, because short selling is much better than a deep out-of-money put option.

• Style Drift- Managers of hedge funds can always change their styles to take advantage of mispricing. In such a case, the original benchmark might no longer be appropriate.

• Portfolio Turnover- Managers might increase the turnover to exploit the volatility in the market and they might stray from their stated strategy. The return earned in such a case might be pure luck…you never know.

4. Evaluating a hedge fund’s performance: There are 3 different benchmarks that can be used: Broad Market Indexes, Hedge Fund Indexes and Risk free return.

Broad Market Index:

Both the Sharpe Ratio and the Jensen’s alpha method pose problems because they use S&P 500 for the evaluation of the performance, which might not be appropriate for evaluating fixed income arbitrage hedge funds. Second, the hedge fund’s beta can change depending upon the change in strategy. Third, alpha changes depending upon the time interval.

It has been found that Merrill Lynch High Yield Index is a good benchmark for fixed income arbitrage funds and Russell 3000 is a good benchmark for various equity funds like long/short equity, market neutral funds, global macro funds or emerging market funds.

Hedge Fund Index:

Different hedge funds have diff. strategies and are difficult to compare. This type of benchmark suffers from data and questionable statistics problem:

Data Problems:

• Voluntary report of performance of hedge funds means that many times, hedge funds with poor performance don’t submit their reports
• The returns of some large hedge funds might be excluded
• self-reported hedge fund data is not confirmed by index providers.

Questionable stats problems:

• Constituent funds change over time, so the index is inconsistent
• funds are subjected to survivorship and backfill bias
• some hedge funds are closed to new investors
• serial correlation in hedge funds lead to low standard deviation
• the historical record of hedge funds is very limited.

Risk Free Rate Method: Many managers feel that if a premium is added to the risk free rate, then it should give a nice assessment for the management and marketing fees and will make for a nice benchmark.

Of the equity funds, market neutral fund has a return that is closest to the risk free rate. Even though these funds are supposed to have zero beta, it is not always so, because if they are neutral on the basis of dollars, then the beta will not be zero. Hence, some risk is always there. Besides, it might also have some unsystematic risk.

On the fixed income side, the arbitrage funds take long positions on corporate bonds and a short position on the treasury bonds and seek to exploit the credit spread. In case of the crisis, if the yield on the corp. bond rises ( price decreases) and the yield on treasury bond falls (price increases) , then they will suffer huge losses. Besides, they also use a very high leverage. So risk free rate is not a good benchmark.

Conclusion: Never use any one benchmark in isolation, instead mix and match all of them. It is necessary to keep in mind the investor’s investment objective, the style, risk and leverage. For equity funds- we should should a weighted average beta to conclude the required return. For fixed income funds, we should multiply the credit spread by the leverage used. In either cases, a benchmark based on several factors may be used.

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Tags: HedgeFunds, Equity Vauation, CFA, Finance, Business, Thoughts

Reading 51: Investment Analysis

The first part talks about different real estate investments like Raw Land, Warehouses, Office Apartments, Residential Apartments, Shopping Malls and Hotels/Motels. The most illiquid is Raw Land, followed by Shopping Centers and Hotels.

The most passive investment is a Warehouse because of the long term lease involved.

Next, we learn how to calculate Cash Flow after Taxes (CFAT) and Equity Reversion After Taxes (ERAT) and then use these along with the NPV and IRR formula to make real estate investment decisions.

For the calculation of CFAT, we use the following steps-

1. Calculate taxes payable using: (Net Operating Income (NOI)- Interest(I)- Depreciation (D))* Marginal Income Tax Rate = Taxes Payable.

2. Then, NOI- Annual Debt Service- Tax payable (from Step 1) = CFAT

ERAT is calculated for the last year of the investment, after it is sold. The recaptured depreciation needs to be calculated-

• When net selling price (Selling price- selling expenses) > Original cost, then the recaptured depr= total accumulated depreciation. (Since the investment has appreciated, the entire depr. needs to be recaptured).
• If Net Selling Price < Original cost, then Recaptured Depr < Accumulated depr. and is calculated as (Net selling price- Adjusted Book Value = Realisd Capital Gain).

The format for arriving at the total tax on realized gain is-

Sales Price
-Expenses associated with Sales
======
= Net Sales price
- Book Value (Original Value- Accum. Depr)
=========
Realized Gain

Now, the tax on realized gain= Tax on Recaptured Depr + Tax on Long term capital gain.

So, calculate the tax on recaptured depr= Tax rate on Recap. Depr * The recap. depr (as illustrated above).

Then, the long term capital gain that should be taxed at the Capital gains tax rate- Realized gain- Recaptured depr. . Then calculate the tax on long term capital gain by using the tax rate for capital gains * total long term capital gain.

ERAT is calculates as Sales price- Sales costs- total mortgage payments- Total taxes (incl. recap. depr. tax and long term cap. gains tax).

The third part of the reading is about NPV and IRR. Same old stuff! For calculating them, use CFAT for the cash flows, and also discount ERAT for the terminal year. The discount rate that is used is called the after-tax discount rate. In case of a conflict, go for NPV (like we learned before).

THE END!

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Tags: RealEstate Valuation, CFA, Finance, Equity Valuation, Business

Reading 49: Residual Income Valuation

1. Residual income= Net Income- Cost of Equity (Equity rate*total equity outstanding)=E-(r*Equity)=(ROE-r)*BV(t-1)

2. Economic Value Added (EVA)= NOPAT -$WACC, where NOPAT= EBIT(1-t)

$WACC= WACC* Invested Capital

Invested capital= Change in NWC+ Net fixed Assets = BV of Long term debt + BV of Equity

Some adjustments that need to be made:

• R&D costs should be capitalized instead of expensed
• Strategic investments that will earn returns in the future should not be charged.
• Amortization needs to be added back to the earnings; goodwill should be capitalized and depreciation should be added back to the invested capital.
• only cash taxes should be considered. Deferred taxes are eliminated.
• Operating leases are treated as capital leases

3. Market Value Added (MVA)= MV of long term debt and MV of long term equity – BV of long term debt and equity (same as invested capital acc. to #2; a.k.a total capital)

4. Single state residual income model:

V0=B0+[(ROE-r)/(r-g)] *B0  (From the equation P0/B0=(ROE-g)/(k-g)

5. Bt=B(t-1)+Et-Dt. The residual income model assumes this clear surplus relationship.

6. In general, V0=B0+ Present Value of (Future residual income). For multi stage RI model, first forecast RI over the short term growth period, and then make some simplifying assumptions over the long term period. The  RI over the long term period is assumed to have constant growth and ROE and is known as continual RI.

The value of continual RI in year (T-1) is RI(t)/(1+r-w) where w= persistance factor and ranges betn. 0 and 1.

Alternate method of finding continual RI= P(t)-B(t) and then discount this back to the present.