Questions and Answers of Investment Risk Management

Derive equation (6.9).\[\left.\frac{\partial}{\partial w_{i}}\left(\sum_{i j}^{n} \sigma_{i j} w_{i} w_{j}\right)^{1 / 2}=\left(\sum_{i j}^{n} \sigma_{i j} w_{i} w_{j}\right)^{-1 / 2} \sum_{j=1}^{n}
Two assets with expected rates of return $\bar{r}_{1}$ and $\bar{r}_{2}$ have identical variances and a known correlation coefficient $ho$. There is a risk-free asset with rate of return $r_{f}$.(a)
Show that for equation (6.10) all rates of return $r$ can be transformed by the linear relation $R=a r+b, a>0$ and that equation (6.10) will still hold for the $R$ 's (although the $v_{i}$ 's will
Two risky assets are derived by a single flip of a coin. For asset $A$, a "heads" outcome pays $\$ 4.00$, while a "tails" outcome pays $\$ 0.00$. For asset B, the corresponding payments are $\$ 3.00$
Assume that the expected rate of return on the market portfolio is $23 %$ and the rate of return on T-bills (the risk-free rate) is $7 %$. The standard deviation of the market is $32 %$. Assume that
Consider a world in which there are only two risky assets, $A$ and $B$, and a risk-free asset $F$. The two risky assets are in equal supply in the market; that is, $M=\frac{1}{2}(A+B)$. The following
Consider a universe of just three securities. They have expected rates of return of $10 %, 20 %$, and $10 %$, respectively. Two portfolios are known to lie on the minimum-variance set. They are
Derive the CAPM formula for $\bar{r}_{k}-r_{f}$ by using Equation (6.9) in Chapter 6.\[\sum_{i=1}^{n} \sigma_{i k} w_{i}=\operatorname{cov}\left(r_{k}, r_{M}\right)\]Apply equation (6.9) both to
Suppose there are $n$ mutually uncorrelated assets. The return on asset $i$ has variance $\sigma_{i}^{2}$. The expected rates of return are unspecified at this point. The total amount of asset $i$ in
In Simpleland there are only two risky stocks, A and B, whose details are listed in Table 7.4.Furthermore, the correlation coefficient between the returns of stocks $A$ and $B$ is $ho_{A
Let $w_{0}$ be the portfolio (weights) of risky assets corresponding to the minimum-variance point in the feasible region. Let $\mathbf{w}_{1}$ be any other portfolio on the efficient frontier.
Electron Wizards, Inc. (EWI) has a new idea for producing TV sets, and it is planning to enter the development stage. Once the product is developed (which will be at the end of 1 year), the company
Prove to Gavin Jones that the results he obtained in Examples 7.5 and 7.7 were not accidents. Specifically, for a fund with return $\alpha r_{f}+(1-\alpha) r_{M}$, show that both CAPM pricing
Suppose there are only two risky assets with expected rates of return $\bar{r}_{1}=0.1, \bar{r}_{2}=0.2$ and covariances $\sigma_{1}^{2}=0.04, \sigma_{2}^{2}=0.09, \sigma_{1,2}=0.03$. The current
Assume the market portfolio has expected rate of return $\bar{r}_{\mathrm{m}}=0.12$ and standard deviation $\sigma_{\mathrm{m}}=0.3$. The risk-free rate is $r_{f}=0.02$. There is another stock,
Let $M$ be a marketed asset that is also a pricing asset such that for every marketed payoff $x$ there holds $P_{x}=\mathrm{E}[M x]$. Show that it follows
A company earns a rate of return of $r_{A}$ and has beta $\beta_{A}$. A fraction $w$ of the assets is owned by bondholders, and the remaining fraction $(1-w)$ is owned by equity holders. Every year,
Consider the pricing formula\[P_{x}=\frac{1}{R}\left\{\bar{x}-\beta_{x, M}\left(\bar{M}-P_{M} R\right)\right\}\]Let $N=a M+b$ for constants $a>0$ and $b$. Show that substitution of $N$ for $M$ yields
Suppose there are two stocks that are uncorrelated. Each of these has variance of 1 , and there are expected returns are $\bar{r}_{1}$ and $\bar{r}_{2}$, respectively. The risk-free rate is $r_{f}$.
Suppose there is a master space $\Omega$ of payoff elements (of finite dimension), of which those in the market are in the subspace $\mathcal{M}$.We may write
Suppose there are two marketed assets, each with price 1 and payoffs $y_{1}$ and $y_{2}$, respectively, with $\bar{y}_{1}=1.4$ and $\bar{y}_{2}=0.8$. Each has a variance of 0.04 , and they are
Firm $X$ is about to be offered publicly, and the investment banking firm that is facilitating the offering is working to determine an appropriate offering price. There is a publicly traded company
Someone who believes that the collection of all stocks satisfies a single-factor model with the market portfolio serving as the factor gives you information on three stocks which make up a portfolio.
Two stocks are believed to satisfy the two-factor model\[\begin{aligned}& r_{1}=a_{1}+2 f_{1}+f_{2} \\& r_{2}=a_{2}+3 f_{1}+4 f_{2} .\end{aligned}\]In addition, there is a risk-free asset with a rate
Suppose there are $n$ random variables $x_{1}, x_{2}, \ldots, x_{n}$ and let $\mathbf{V}$ be the corresponding covariance matrix. An eigenvector of $\mathbf{V}$ is a vector $\mathbf{v}=$
Let $r_{i}$, for $i=1,2, \ldots, n$, be independent samples of a return $r$ of mean $\bar{r}$ and variance $\sigma^{2}$. Define the estimates\[\begin{aligned}\hat{\bar{r}} & =\frac{1}{n}
The data here show the rate of return of a stock and the corresponding value of a factor $F$. In the model\[r_{i}=a+b \times F+\varepsilon_{i}\]find the best values of $a$ and $b$ (which minimize the
Assume that the following two-index model describes returns:\[\bar{r}_{i}=r_{f}+b_{i 1} \lambda_{1}+b_{i 2} \lambda_{2}\]Assume that the following three portfolios are observed:(a) According to APT,
Suppose that sixteen stocks have been identified whose rates of return satisfy\[\overline{r_{i}}= \pm \alpha+f+\varepsilon_{i}\]where $\alpha>0$. Eight of the stocks use the + sign and the other
Suppose a stock's rate of return has annual mean and variance of $\bar{r}$ and $\sigma^{2}$. To estimate these quantities, we divide 1 year into $n$ equal periods and record the return for each
A record of annual percentage rates of return of the stock $S$ is shown in Table 9.5(a) Estimate the arithmetic mean rate of return, expressed in percent per year.(b) Estimate the arithmetic standard
Gavin Jones figured out a clever way to get 24 samples of monthly returns in just over one year instead of only 12 samples; he takes overlapping samples; that is, the first sample covers Jan. 1 to
For Example 9.3, represent the uncertainty in the expected returns of the two stocks in the form of u +e, where E[e] = 0 with covariance matrix of e equal to Q. Example 9.3 (Various angles) Consider
In Table 9.2, suppose the variance of the two assets are incorrectly estimated to be .044 instead of the actual .04 (which is a 10% error). Find the “think” value for the tangent of the angle of
Plot the value of “actual”— “theory” for Example 9.3 for e in the range 0 ≤ e ≤ .20. Explain the rather dramatic character of the plot. Example 9.3 (Various angles) Consider the case of
Suppose there are three assets with expected rates of return r1, = 0.10, r2 = 0.07, r3 = 0.14. Each has a standard deviation of .20, and all pairs have correlation coefficient ρ = .4. There is a
Consider this problem:Let “think” be the value with e, and let “theory” be the value with e = 0. Now assume that e is random with expected value zero. Show that the expected value of
Discuss capital controls that could be beneficial to frontier and emerging economies.
Market transparency in the credit market may be related to the bank’s optimal loan and hedging transactions. Lower credit risk could be due to more market transparency and lead to a higher loan
Regulators can only constrain the behavior of individual banks through incentives such as capital and liquidity requirements but they cannot affect systemic risk directly. Identify the problems that
Discuss the uses and limitations of the standard deviation (volatility) as risk measure.
Discuss the advantages and disadvantages of VaR as risk measure.
Explain why basing risk management on the profit-and-loss distribution is reasonable.
Discuss the different roles of a risk measure in the context of financial optimization.
Identify the drawbacks of the described profit-and-loss distributional approach.
How does hedging differ from insurance?
Why does hedging create value only if the firm’s cost structure is convex in the hedgeable risk?
Explain whether financial risk management allows a better assessment of managerial quality.
Discuss the following assertion. Entering into a financial derivative position creates no value directly and destroys value in the short run. Thus, the only reason that non-financial firms use such
Given that accounting is backwards looking, explain why accounting accruals are informative about the future.
Given that investors appear to process accounting information imperfectly, discuss one price anomaly and how investors may profit from using this anomaly.
List several useful variables in predicting large corporate frauds and discuss the implications for investment decisions.
Identify the conditions under which forecasting of firm-specific volatility may or may not be valuable for investment decisions.
Before January 1, 2005, Norwegian Telenor ASA prepared its financial statements according to Norwegian Generally Accepted Accounting Principles (N GAAP). Starting in 2005, Telenor ASA used
Practitioners have used and disclosed VaR since the 1990s. The Basel Committee on Banking Supervision has proposed replacing VaR with a different one-sided risk measure called expected shortfall,
Explain how demographic shifts might change the aggregate supply of the willingness to bear risk and affect asset prices.
Identify the tasks that gain importance for investment advisors and portfolio managers if apparent excess returns turn out to have their origin in previously unknown systematic risk factors.
Discuss whether constructing a well-diversified portfolio is possible that completely hedges all market risks including beta, value, and size risks. Indicate whether such portfolios would be
Explain how the state of the economy might affect market risk and what caution an investment advisor might give to a potential client on the risk exposure of a portfolio.
Explain the difference between “point-in-time” and “through-the-cycle” credit risk indicators.
Explain a methodology that can be used to build a transition matrix from a history of 25 years of rating information and whether this matrix can be used to derive default probabilities for longer
Define VaR and discuss how this measure is used in practice.
Identify the key inputs to a credit portfolio simulation model and three practical areas of usage for such models.
Explain one main difference between the Merton model and a statistical credit scoring model such as the linear logit model for estimating probabilities of default.
List and discuss three pillars of the Basel II Accord framework.
List two methods for calculating operational risk capital and discuss the differences.
Identify and discuss issues with using VaR and ES for measuring operational risk.
Discuss the need to combine internal data with external data and scenario analysis for estimating operational risk.
Define liquidity as related to finance.
Discuss how funding liquidity and market liquidity are linked.
Discuss why measuring liquidity is difficult.
Identify the most reliable illiquidity measures among those used in empirical studies and justify why this is the case.
Analysts often argue that a country cannot default on its local currency bonds because it has the power to print more currency to pay off its debt. Explain why this argument is incorrect.
Discuss whether sovereign ratings are good measures of sovereign default risk.
The sovereign default spread for a government can be estimated from sovereign bonds in U.S. dollars or the sovereign CDSmarket. Explain why the two approaches may result in different answers.
Given that some country equity risk is diversifiable to global investors, discuss whether it should be included in the price.
ERPs in emerging markets converged toward ERPs in developed markets between 2008 and 2012. Explain reasons for this trend.
Discuss whether analysts should use models that assume U.S. companies are not exposed to emerging market risk.
All companies in an emerging market are not equally exposed to the risk in that emerging market. Identify factors that explain differences in country risk exposure across companies and discuss how to
Discuss how systemic risk differs from systematic risk.
Give some examples of how sources of systemic risk are connected.
Discuss the problem of assessing systemic risk when only the risk of individual banks can be determined.
Discuss the importance of framing or mental accounting from a behavioral risk perspective and its relationship to Benartzi and Thaler’s explanation of the equity premium puzzle.
Explain whether the absence of an arbitrage opportunity necessarily implies that markets are efficient.
Explain the implications of familiarity bias for asset allocation.
Explain how pareidolia and apophenia can be observed in financial markets.
Explain how the anchoring heuristic is related to an agent’s overconfident behavior and illustrate how overconfidence affects trading behavior.
Discuss the role of the board in an organization.
Discuss the factors making a board effective or ineffective.
Identify and explain conditions in which boards experience failure.
Identify and explain positive signals of effective governance.
Explain why an inflationary scenario can be expected after three decades of moderate price changes.
Discuss how central banks strategies toward inflationary concerns developed since the 1970s.
Discuss how standard investment instruments perform in an inflationary scenario and the difficulty in using these instruments as an inflation hedge.
Discuss why and how investors can use trend-following strategies as a hedge against inflation.
Define risk aggregation and discuss its importance.
Explain the structural approach used to measure credit risk.
Explain the approaches used to measure market risk.
List various measures used in reporting total risk and discuss their relative strengths and weaknesses.
List various approaches for risk aggregation and discuss pros and cons of each.

Showing 300 - 400 of 477