# Actuarial Science CT-8 Financial Economics Quick Review

Writing Actuarial Science CT-8 paper this diet or have you cleared Ct-8 before and have your interview? Do you have less time that you can’t go through the whole study material to mug up the summary of the syllabus? And even if you have time you don’t want to go through the whole study material? Don’t worry here is the solution for this. You are at the right place. You can have a quick revision of the CT-8 here with very less time.

So, let’s find the important questions that could be asked of you in examinations and/ or in the interviews:

Q: What are the three forms of the Efficient Market Hypothesis (EMH)?
Ans: The three forms of the Efficient Market Hypothesis are as follows:

1. Strong form EMH: market prices incorporate all information, both publicly available and also that available only to insiders
2. Semi-strong form EMH: market prices incorporate all publicly available information.
3. Weak form EMH: the market price of an investment incorporates all information contained in the price history of that investment.

Q: What is the difference between active and passive investment management?
Ans: Active fund managers attempt to detect exploitable mispricing. Passive fund managers simply aim to diversify across a whole market.

Q: What do you mean by utility functions?
Ans: In the application of utility theory to finance and investment choice, it is assumed that a numerical value called the utility can be assigned to each possible value of the investor’s wealth by what is known as a preference function or utility function. For example, in a certain world Investor X might have a utility function of the form:

U(w) =log(w)

where w is his current or future wealth.

Q: Define the expected utility theorem.
Ans: The theorem has two parts.

1. The expected utility theorem states that a function, U(w), can be constructed representing an investor’s utility of wealth, w, at some future date.
2. Decisions are made on the basis of maximizing the expected value of utility under the investor’s particular beliefs about the probability of different outcomes.

Q: Name the four axioms for the derivation of the expected utility theorem?
Ans: the four axioms for the derivation of the expected utility theorem are

1. Comparability: An investor can state a preference between all available certain outcomes.
2. Transitivity: If A is preferred to B and B is preferred to C, then A is preferred to C.
3. Independence: If an investor is indifferent between two certain outcomes, A and B, then he is also indifferent between the following two gamblers (or lotteries):
• A with probability p and C with probability (1-p)
• B with probability p and C with probability (1-p)
4. Certainty equivalence: Suppose that A is preferred to B and B is preferred to C. Then there is a unique probability, p, such that the investor is indifferent between B and a gamble giving A with probability p and C with probability (1-p).

Q: Define stochastic dominance?
Ans: Absolute dominance exists when one investment portfolio provides a higher return than another in all possible circumstances. Clearly, this situation will rarely occur so we usually need to consider the relative likelihood of outperformance; ie stochastic dominance.

We consider two investment portfolios, A and B, with cumulative probability distribution functions of returns FA and FB respectively.

Q: Define first-order stochastic dominance theorem?
Ans: The first-order stochastic dominance theorem states that assuming an investor prefers more to less, A will dominate B (ie the investor will prefer portfolio A to portfolio B).

This means that the probability of portfolio B producing a return below a certain value is never less than the probability of portfolio A producing a return below the same value, and exceeds it for at least some value of x.

Q: Define second-order stochastic dominance theorem?
Ans: The second-order stochastic dominance theorem applies when the investor is risk averse as well as preferring more to less.

Q: Write Common themes found in research on behavioral finance?
Ans: Common themes found in research on behavioral finance include:

• prospect theory
• framing (and question-wording)
• myopic loss aversion
• estimating probabilities
• overconfidence
• mental accounting
• the effect of options.

Q: What do you understand by mean-variance portfolio theory?
Ans: Mean-variance portfolio theory, sometimes called modern portfolio theory (MPT), specifies a method for an investor to construct a portfolio that gives the maximum return for a specified risk or the minimum risk for a specified return.

If the investor’s utility function is known, then MPT allows the investor to choose the portfolio that has the optimal balance between return and risk, as measured by the variance of return and consequently maximizes the investor’s expected utility.

Q: What are the main assumptions of mean-variance portfolio theory?
Ans: the main assumptions of mean-variance portfolio theory are

• all expected returns, variances and covariances of pairs of assets are known.
• investors make their decisions purely on the basis of expected return and variance
• investors are non-satiated
• investors are risk-averse
• there is a fixed single-step time period
• there are no taxes or transaction costs
• assets may be held in any amounts, ie short-selling is possible, we can have infinitely divisible holdings, and there are no maximum investment limits.

Q: When the portfolio is said to be efficient and inefficient?
Ans: A portfolio is inefficient if the investor can find another portfolio with the same (or higher) expected return and lower variance, or the same (or lower) variance and higher expected return.

A portfolio is efficient if the investor cannot find a better one in the sense that it has either a higher expected return and the same (or lower) variance or a lower variance and the same (or higher) expected to return, ie an efficient portfolio is one that isn’t inefficient.

Q: Define multifactor models and types of multifactor models?
Ans: A multifactor model of security returns attempts to explain the observed historical return by an equation where:

• Ri is the return on security i
• ai, ci are the constant and random parts respectively of the component of return unique to security i
• I..IL are the changes in a set of L factors which explain the variation of Ri about the expected return ai
• bi,k is the sensitivity of security i to factor k.

Three types of multifactor models are as follows:

1. Macroeconomic factor models: These use observable economic time series as the factors. They could include factors such as the annual rates of inflation and economic growth, short-term interest rates, the yields on long-term government bonds, and the yield margin on corporate bonds over government bonds.
2. Fundamental factor models: Fundamental factor models are closely related to macroeconomic models, but instead of (or in addition to) macroeconomic variables the factors used are company-specific variables. These may include such fundamental factors as:
• the level of gearing
• the price earnings ratio
• the level of research and development spending
• the industry group to which the company belongs.

The models are constructed using regression techniques.

3. Statistical factor models: Statistical factor models do not rely on specifying the factors independently of the historical returns data. Instead, a technique called principal components analysis can be used to determine a set of indices which explain as much as possible of the observed variance.However, these indices are unlikely to have any meaningful economic interpretation and may vary considerably between different datasets.

Q: Explain the definition and basic properties of standard Brownian motion?
Ans: Standard Brownian motion (also called the Wiener process) is a stochastic process {Bt, t >0} with state space S = R (the set of real numbers) and the following defining properties

• Bt has independent increments
• Bt has stationary increments
• Bt has Gaussian increments
• Bt has continuous sample paths
• B0=0

Q: Define arbitrage opportunity?
Ans: An arbitrage opportunity is a situation where we can make an arbitrage opportunity is a situation where we can make a more precise, an arbitrage opportunity means that:

• we can start at time 0 with a portfolio that has a net value of zero (implying that we are long in some assets and short in others).
• at some future time T:
• The probability of a loss is 0
• The probability that we make a strictly positive profit is greater than 0.

Q: Define Put-call parity?
Ans: Put-call parity is a theoretical relationship between the price of a call option and a put option on a share. The options involved have the same exercise price and exercise date.

It assumes that security markets are arbitrage-free and that there is a constant and known risk-free rate of return that can be earned on deposits. However, it makes no assumptions about the nature of the process determining share prices.

Q: What are the main assumptions of the binomial model?
Ans: The main assumptions of the binomial model are:

• there are no trading costs or taxes
• there are no minimum or maximum units of trading
• stock and bonds can only be bought and sold at discrete times 1, 2, …
• the principle of no arbitrage applies.

Q: Define a replicating portfolio and differentiate it from hedging portfolio?
Ans: Any portfolio is called a replicating portfolio if it replicates, precisely, the payoff at time 1 on the derivative without any risk.

A replicating portfolio will always precisely reproduce the relevant payoff or cash flow. A hedging portfolio aims to reduce the amount of risk relating to a derivative strategy but is not guaranteed to reproduce the payoff or cashflow precisely. Furthermore, a replicating portfolio is only a hedging portfolio if the position taken in it is opposite to that of the payoff or cash flow which it aims to reproduce.

Q: What are the main assumptions of the Black-Scholes model?
Ans: The assumptions underlying the Black-Scholes model are as follows:

1. The price of the underlying share follows a geometric Brownian motion.
2. There are no risk-free arbitrage opportunities.
3. The risk-free rate of interest is constant, the same for all maturities and the same for borrowing or lending.
4. Unlimited short selling (that is, negative holdings) is allowed.
5. There are no taxes or transaction costs.
6. The underlying asset can be traded continuously and in infinitesimally small numbers of units.

Q: When the market is said to be complete?
Ans: The market is complete if for any such contingent claims X there is a replicating strategy.

This is important because it means that, in a complete market, we will always be able to price a contingent claim X, such as a derivative, based on the arbitrage-free approach and using a replicating strategy.

Q: Define equivalent measures?
Ans: Two measures P and Q which apply to the same sigma-algebra F are said to be equivalent if for any event E in F:

P(E) >0 if and only if Q(E) >0

Where P(E) and Q(E) are the probabilities of E under P and Q respectively.

Q: What are the outcomes of a default?
Ans: The outcome of a default may be that the contracted payment stream :

• Is rescheduled
• Is canceled by the payment of an amount which is less than the default free value of the original contract
• continued but at a reduced rate
• Is totally wiped out.

Q: Define a credit event?
Ans: A credit event is an event that will trigger the default of a bond and includes the following:

• failure to pay either capital or a coupon
• loss event
• bankruptcy
• the rating downgrade of the bond by a rating agency such as Standard and Poors or Moody’s.

Q: What are the different credit risk models?
Ans: Different credit risk models are as follows:

1. Structural models: Structural models are explicit models for a corporate entity issuing both equity and debt. They aim to link default events explicitly to the fortunes of the issuing corporate entity.The models are simple and cannot be realistically used to price credit risk. An example of a structural model is the Merton model.
2. Reduced-form models: Reduced-form models are statistical models, which use observed market statistics rather than specific data relating to the issuing corporate entity. The market statistics most commonly used are the credit ratings issued by credit rating agencies such as Standard and Poors and Moody’s.The credit rating agencies will have used detailed data specific to the issuing corporate entity when setting their rating. They will also regularly review the data to ensure that the rating remains appropriate and will re-rate the bond either up or down as necessary.
3. Intensity-based model: An intensity-based model is a particular type of continuous-time reduced form model. It typically models the “jumps” between different states (usually credit ratings) using transition intensities.

This is all from my side. Apart from this, I would suggest you not to learn things, try to understand the terms and models. Hope this helps.

GOOD LUCK