Derivates Completed

I’m done with this part. I found the Swaps chapter to be a little confusing. Even the one on Credit Default Swaps was totally new and took me some time to understand. I’ll need to keep revising the formulas. Other than that, futures, forwards, options…etc. were quite okay for me.

I’m starting Quants tomorrow and hope to get done with it by this weekend.

Delurkers, Come Out!

I didn’t do any studies today, except for a couple of problems. So, no way that I’m going to complete everything by tomorrow. Ha!

Because of that, I’m pissed off. The stats of this blog has been rising steadily and the funny thing is that not many of you people who are reading this post now take the time to comment!

So if you’re reading my blog, it would be great if you could come out and comment. Thanks!

Reading 62: Forward Markets and Contracts

I started studying Derivatives today and it’s been an easy ride because I already know everything in this portion of the syllabus. Heh heh 😀 Still, completing it by 1/31 seems like madness, unless I do around 1.5 Readings everyday on an average..

I won’t be posting any notes for this reading, because it’s calculation based and I’m better off making index cards. If you want to read, then I recommend Matt’s post on this topic. He’s done an amazing job. (Matt can be found in my Blogroll). In fact, I might just revise the key concepts from his blog and then go to my index cards for the precise formulae.

Happy Reading!

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!

Quick Update on PM

Allright! Three cheers for me 😀 Just got done with Port. Management. However, I’m thinking of spending this day finishing off some problems based on Treynor Black Model, because of which lots of people got screwed last June. I plan to post some notes on this part and Reading 68 (which I’d not done before) today. I also want to re-visit Reading 68 using the Curriculum. Tomorrow onwards, I’m going to start off with Derivatives. Technically, I’m supposed to finish it by 1/31. That gives me only four days…kinda impossible…but might not be, because I took a look at the topics, and I already know half of them, thanks to my Derivatives course in MBA. So, let’s hope for the best.

I really really need to finish off Econ, Stats and Fixed Income by the end of Feb, so that I can revise and re-revise for the remaining three months…which I’ll badly need (because I don’t remember much).

Think I’ve been rambling too much. Any of you reading this- please feel free to comment and let me know about your progress.

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.

Reading 70: International Asset Pricing

I’m going to cover only the first part of the reading here. Btw, you might want to study from the Official Curriculum the entire Portfolio Management portion. Schweser sucks, at least for this part. I found several rounding and formula errors while studying this reading. So…just a small warning.

1. International markets are integrated and efficient if the securities with the same risk characteristics have the same expected return all over the world.

They are segmented and inefficient if the securities with similar characteristics sell at different exchange rate- adjusted prices in different countries, thus violating the law of one price. This is often the case when we deal with emerging markets.

There are six impediments to international capital mobility- Psychological barriers, legal restrictions, transaction costs, discriminatory taxation against foreign income, political risks and foreign exchange risks.

Intl. integration requires only a sufficient flow of capital to make the world market efficient and to eliminate mispricing among countries.

2. Expected return on an unhedged foreign investment:

E(R)= E(Rfc)+ s, where E(R)= expected return in DC , E(Rfc)= Expected return in FC and s= appreciate/depr, calculated as (S1-S0)/S0

OR

E(R)=R(dc) +FCRP, Rdc= risk free domestic interest rate and FCRP= Foreign currency risk premium. (Take a look at #7 regarding how to calculate FCRP)

Expected return on a hedged foreign investment:

E(R)=E(Rfc)+ (F-s)/s, where F= Locked in forward rate

Both F and S are DC/FC. (F-S)/S is the forward risk premium/discount, which can be found out from the Interest Rate Parity Equation: F=(S*(1+rDC))/(1+rFC) or approx, (F-S)/S= (Rdc-Rfc).

3. Extended CAPM is the domestic CAPM, with the domestic Rf as the Rf rate and the market portfolio is composed of all the risky assets of the world.

4. This extension of CAPM can be justified with addl. two more assumptions:

a. Investors throughout the world have identical consumption baskets

b. PPP holds (the real prices of consumptions goods are identical across countries).

5. Real exchange rate (X)= (S dc/fc)(P fc/dc), where S= nominal exchange rate and P= Price level

6. Also, x (real rate) = s- (Idc-I fc) , where s= change in nominal rate and (I dc- I fc) = inflation differential rate. If PPP holds, then, x=0% and the nominal exchange rate movement (DC/FC) = Inflation rate differential. If this doesn’t happen, then any such real exchange rate movement (means nominal rate movement that is not explained by the inflation % change) would violate the assumptions supporting the domestic CAPM extension, which is the same as real foreign exchange currency risk.

Hence, in the absence of real exchange currrency risk, CAPM extension holds, otherwise not!

Part II (01/25/08)

7. FCRP (Foreign Currency Risk Premium) is calculated as: E(s)- (Rdc-Rfc), where E(s)= (S1-So)/S0 or the currency appreciation/depreciatio; and (Rdc-Rfc) is the approx. forward premium or discount. Alternate method: [E(S1)-F]/S0

8. Since PPP does not always hold in the real world, we need to use the International CAPM Model (ICAPM), which is almost the same as domestic CAPM, except that it also factors in the FCRP and the sensitivity to each FCRP (gamma).

Limitation: Applies only to an integrated world capital market with currency hedging available.

9. Other forms of market imperfections and constraints cannot be easily integrated with the equilibrium asset pricing framework.

10. Local currency exposure measures the sensitivity of the local asset return to the local currency value and is found by time series regression. Can either be zero correlation (no relation between return and value), negative correlation (value of the currency increases, then the stock return decreases), or positive correlation (both currency value and the stock return increase).

11. For an investor, the domestic currency exposure= 1+ local currency exposure. It only depends upon the value of the local currency and not the local asset return.

12. If exchange rate movements only reflect inflation rate differentials , that is PPP holds, then there is no specific influence on the economy. Real exchange rate movements, however, have an impact on the equity prices, depending on currency exposures.

13. Two models for explaining the effect of the exchange rate movement on the domestic economic activity:

The traditional model: A decline in real exchange rate for a country creates problems in the short term, because the trade deficit increases –>GNP decreases because imports become costly, production cost increases etc. –> eventually offset by the improved international competitiveness and export demand until PPP is restored. Thus, the traditional model predicts a negative currency exposure.

The Money Demand Model: Predicts a positive currency exposure. An increase in the real exchange rate of the country will cause in increase in the stock returns because of the increase in the currency demand.

Caution: A drop in the value of an emerging market’s currency is often a signal that the country is running into severe problems.

14. Currency Exposure for Bonds: There are two models again-

a. The Free Market Model– Predicts a negative currency exposure. Increase in real interest rate will cause an increase in the currency value, but the bond price will go down.

b. The Govt. Intervention Method (Leaning against the Wind)– Predicts a positive currency exposure. Increase in the stock price will make the Govt . reduce the real interest rates, thus inflating the bond prices.

15. Currency Exposure of Individual Firms- Can be estimated by regressing the company’s stock’s returns against market returns and currency returns. Can be fine tuned by a detailed analysis of the source of sales, profit margins , costs, geographical origin of the sales, costs etc.

Level-I results for December 2007 Just Declared

Lots of people whom I know from the Analyst Forum cleared it. This comes at the right time…just when I started losing my interest. It has brought me back to the “CFA World” with a jolt and my interest in those romantic books has been renewed.

Expect some sexy action here! CFA Insti- Watch out for me.

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

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