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» Q&A: How to increase the power of a statistical test?

» Q&A: Suppose there is a value-weighted market index...

» Q&A: An analyst is trying to prove that the annualized return of S&P 500...

» Q&A: Give some examples of when a nonparametric test should be used.

» Q&A: What does it mean for the price of...

» Q&A: Which form of the efficient market hypothesis...

» Q&A: List some of the assumptions technical analysis makes...

» Q&A: Give an example how portfolio managers can beat...

» Q&A: List some of the assumptions fundamental analysis makes....

» Q&A: What are some of the things generally included in a bond indenture?

### Q&A: How to increase the power of a statistical test?

*Answer*: One way is to increase the significance level, therefore reducing the risk of a Type II error. The downside is it also increases the risk of a Type I error.

*Bonus Points*

- The power of a test is the probability of correctly rejecting a false null hypothesis: 1 - Type II error probability.
- If the power of an experiment is low, then there is a good chance that the experiment will be inconclusive and need to redesigned.
- Power is not about whether or not the null hypothesis is true. It is the probability the data gathered in an experiment will be sufficient to reject the null hypothesis. The experimenter asks the question: If the null hypothesis is false with specified population means and standard deviation, what is the probability that the data from the experiment will be sufficient to reject the null hypothesis?

*Category: C++ Quant > Finance > Quantitative Analysis*

### Q&A: Suppose there is a value-weighted market index...

composed of 100 shares of stock A selling for $100, and 2000 shares of stock B selling for $25. What's the rate of return if stock A increases by 10%, and B increases by 20%?

*Answer* :

- the new market value = 100*(1+10%)*100 + 25*(1+20%)*2000 = 71000
- RoR = (71000-60000)/60000 = 18.3%

*Bonus Points*

- A value-weighted market index is generated by deriving the initial total market value of all stocks used in the series. The importance of individual stocks in the sample depends on the market value of the stocks. There is an automatic adjustment for stock splits and other capital changes in this series.
- Standard & Poor's 500 Composite Index: based upon 500 firms from NYSE and OTC. The number of stocks in the index is different. The source of the sample is also different. However, the index does not reflect cash dividends paid out by those firms.
- NASDAQ Composite: Based on almost 5,000 OTC firms.
- Amex Market Value

- Firms with large market value have greater impact on the index than firms with small market value. Thus, over time the large market value stocks will dominate changes in a market-value-weighted series.

*Category: C++ Quant > Finance > Financial Markets*

### Q&A: An analyst is trying to prove that the annualized return of S&P 500...

...is greater than 15%. Explain how a Type I and Type II errors could have been made.

*Answer* :

- H(0) = d <= 15%, H(1) = u > 15%
- Type I: Concluding that the return is greater than 15% when in fact it's less than 15%.
- Type II: Going along with the return is less than 15% when in fact it's greater than 15%.

*Bonus Points*

- A Type I error is rejecting H0 when H0 is in fact true.
- A Type II error is failing to reject H0 when H0 is in fact false.
- "Going along" means you can't conclude nor reject it.

*Category: C++ Quant > Finance > Quantitative Analysis*

### Q&A: Give some examples of when a nonparametric test should be used.

*Answer*

- When the data is in the form of rankings (ordinal-scale data): ie. rank the performance of investment managers
- When the data does not involve a parameter: ie. evaluate whether or not an investment manager has had a statistically significant record of consecutive successes
- When The distribution of the underlying population is unknown (ie. not normal). Other tests, such as a median test or the sign test, can be used in place of t-tests for means and paired comparisons, respectively.

*Bonus Points*

- Parametric tests are concerned with the values of parameters, such as means or variances. Parametric tests make assumptions about the distribution of the population underlying the sample from which test statistics are derived.
- In general, parametric tests have stricter assumptions, and when met, allow for stronger conclusions. Non-parametric tests have broader applicability.

*Category: C++ Quant > Finance > Quantitative Analysis*

### Q&A: What does it mean for the price of...

... an instrument to follow a random walk?

*Answer* : Successive price changes are independent of each other (ie. no correlation)

*Bonus Points*

- New information about securities comes to the market in a random fashion, and the timing of the announcement is generally independent of others.
- Due to competition, security prices adjust rapidly to the arrival of new information, and the current prices reflect all avaiable information, thus making the capital market efficient.
- The price adjustment is unbiased: sometimes the market will overadjust and/or underadjust, but you cannot predict its behavior.
- The expected returns should match its perceived risk.

*Category: C++ Quant > Finance > Financial Markets*

### Q&A: Which form of the efficient market hypothesis...

...is widely believed to be true for S&P 500?

*Answer* : both the weak form and semi-strong form of EMH, since S&P 500 is one of the most widely tracked and analyzed index.

*Bonus Points*

- Three versions of the EMH: differ only in how each defines the meaning of "all available information"
- The weak-form hypothesis: "all available information" refers to market data, like past prices, trading volume. Implies trend analysis is meaningless.
- The semistrong-form hypothesis: in additon to market data, it also refers to all publicly available information regarding the prospects of a firm, like product line, quality of management, patents held, earning forecasts. Implies that an investor cannot achieve risk-adjusted excess returns using important public information.
- The strong-form hypothesis: in additon to the above, it includes insider information. Assumes perfect markets, in which all information is cost free and available to everyone at the same time. In contrast, in an efficient market prices adjust rapidly to new public information.

*Category: C++ Quant > Finance > Financial Markets*

### Q&A: List some of the assumptions technical analysis makes...

...in regard to the notion of efficient markets.

*Answer*

- The process of disseminating new information takes time.
- Stock prices move to new equilibriums in a gradual manner.

*Bonus Points*

- Technical Analysis can generate abnormal returns by detecting the significant stock price changes before others do.
- Technical analysts do not believe any form of the EMH (no, no even the weak form), although EMH proponents do not rule out excess returns from technical analysis since markets do not adjust perfectly, leaving the possibility of over- or under-adjustment
- Intra-day technical indicators and trading rules are good examples. The opportunities do not last long and so are generally only available to market participants who are continually trading.

*Category: C++ Quant > Finance > Financial Markets*

### Q&A: Give an example how portfolio managers can beat...

...a buy-and-hold strategy on a risk-adjusted basis.

*Answer* : When the market fails to adjust prices rapidly to public information, porfolio managers can achieve superior investment performance with the help of superior analysts - someone who can time major market trends or identify undervalued securities.

*Bonus Points*

- A profolio manager can manage actively, without changing the risk preferences of the client
- looks for undervalued securities based upon superior fundamental analysis (including predicting earnings surprise). Mid-cap stocks are good candidates: generally not followed by as many analysts, more likely to be trading in a less efficient market and yet still liquid enough
- attempts to time the market wherein asset allocation is shifted between aggressive and defensive positions

- A portfolio manager can manage passively
- Determine and quantify his risk preferences;
- Construct the appropriate risk-level portfolio by dividing the total portfolio between lending or borrowing risk-free assets and a portfolio of risky assets.
- Diversify completely on a global basis to eliminate all unsystematic risk.
- Maintain the specific risk level by rebalancing when necessary.
- Minimize taxes and total transaction costs (reduce trading turnover and trade relatively liquid stocks to minimize liquidity costs).

- A portfolio manager can also invest in index funds: match the market at the lowest cost

*Category: C++ Quant > Finance > Financial Markets*

### Q&A: List some of the assumptions fundamental analysis makes....

...in regard to the notion of efficient markets.

*Answer* :

- At any time, there is a basic intrinsic value for the aggregate stock market, various industries, or individual securities.
- These values depend on underlying economic factors such as cash flows and risk variables.
- Though market price and the intrinsic value may differ across time, the discrepancy will get corrected as new information arrives.

*Bonus Points*

- Fundamental Analysis can generate abnormal returns by accurately estimating the intrinsic value and making superior market timing decisions (ie. predict earnings surprises) or acquiring undervalued securities.
- Aggregates market analysis, industry analysis, company analysis and portfolio management, uses historical data to estimate the relevant variables
- Market analysis: estimate the relevant variables that cause long-run trends of market movements.
- Industry and company analysis: estimate future values for variables that influence rates of return and predict future earnings surprises. Pay more attention to areas where the market is inefficient, such as stocks that are neglected by other analysts, stocks with high book value/market value ratios, and stocks with small market capitalization.

*Category: C++ Quant > Finance > Financial Markets*

### Q&A: What are some of the things generally included in a bond indenture?

*Answer*

- The basic terms of the bond.
- Details of the protective covenants.
- Sinking fund arrangements.
- Call provisions.

*Bonus Points*

- A bond indenture is a written agreement between the issuer and holders regarding promises (of the issuer) and rights (of the bondholders).
- In a bond indenture, there are two types of covenants
- Affirmative covenants: set forth certain actions that the borrowers must take, such as paying interest and principal on a timely basis, submitting periodic reports to a trustee for evaluation of the issuer's compliance with the indenture, Maintaining a satisfactory working capital ratio (aka financial convenant).
- Negative covenants: certain limitations and restrictions on the borrower's activities, such as the borrower's ability to incur additional debt unless certain tests are met, sale of assets.

- Negative covenants place direct restrictions on management actions and thus play a more significant role than affirmative covenants in loan agreements.
- When the debtor has violated one or more covenants in a loan agreements but continues to make all payments on a timely basis, it's known as "technical default".

*Category: C++ Quant > Finance > Debt*