# 查看完整版本 : Finance 功課一問( EF4331)

## Finance 功課一問( EF4331)

The Excel spreadsheet for the case contains:
[list]                                                [*]  Monthly stock price indexes denominated in local currencies for 22 major countries,beginning-of-month, from December 1981 through February, 2009. Through 2001, theseare the FT Actuaries indexes published daily in the Financial Times. Subsequent to 2001,these are the broadest market indexes provided by GlobalFinData.com and DataStream.They are value-weighted indexes of the largest and most liquid stocks in each national market.[*]Spot foreign exchange rates (foreign currency unit per USD) over the same period.[list=1]                                                [*]Calculate the mean return and volatility (i.e., standard deviation) of return, for all 22 developed countries from the perspective of a U.S. Dollar-based investor (i.e., using Dollar-denominated returns).
(a) First, convert stock price indexes into USD using the spot foreign exchange rates.
(b) Second, calculate the natural logarithmic rate of returns for each index price overtime:
ri,t = ln(Si,t/Si,t−1)where Si,t denotes an index price for country i at time t.[*]  Form an equal-weighted (by country) world market index in Dollars. Calculate the market risk (CAPM β) for each country against the world index and discuss the empirical findings.[list=1][*](a) To calculate the equal-weighted world market index return, simply take the mean of the index returns across all countries for each month.[*]recall the β = Cov(ri,rM)/Var(rM)  ,  where rM is the market return and ri is country i’s return.[*] Calculate the covariance matrix for the 22 countries.[*]  For the next several questions, choose 4 countries from the list of 22 countries that youthink would give an investor the best tradeoff between risk and return. The fifth countryindex in your client’s portfolio will be the US index. You have a client who would liketo diversify internationally, but does not feel comfortable with more than 5 countries intheir portfolio since they would like to follow the news that might affect their investments.Explain your choice of countries in 300 words or less.[*]   Find the portfolio weights on these 5 countries’ indexes that would have minimized total volatility for a U.S. investor. Short positions are allowed. In Modern Portfolio Theory,we solve the following:[list=1][*]arg min Var(rp)=arg minW′VW, subject to WW
W′R = μpW′1 = 1
where rp is the portfolio return, V is the covariance matrix (we estimate this with historical data), W is a vector of portfolio weights, R is a vector of mean returns of every portfolio asset (we estimate this with historical data), and 1 is a vector of ones. The first constraint(W′R = μp) requires that our portfolio earn at least μp on average, which we set. The second constraint (W′1 = 1) requires that our portfolio weights add up to 1. This is a constrained minimization problem that can be solved using Lagrange multipliers. We skip the derivation here. The optimal weights are:
W∗ =V−1 R 1  R′V−1R 1′V−1R −1 μp 1′V −1R 1′V −11 1
=V−1 R 1  a b −1 μp bc1
W∗ is a vector of portfolio weights that minimizes the variance of our portfolio while maintaining an average return of μp. For the rest of this case study, assume μp is equal to the average return of the US equity index.[/list]
[/list]
[/list]
[list][*]6.   Find the maximum net return improvement that a U.S. investor would have gained by investing in these 5 countries as opposed to domestically. Find the maximum net reduction in risk that would have been obtained by a U.S. investor who diversified into these 5country indexes. Note that using W∗, the variance of our portfolio is[list=1][*]Var(rp) =( a − 2bμp + cμ2p)/(ac−b2)[/list]
7.  Plot the efficient frontier for a US investor with these 5 country indexes as their opportunity set. That is, plot the relationship between Var(rp) (x-axis) and μp (y-axis) from the equation above.  8.                                      [*]8.  You are now allowed to include the 4 (or fewer) foreign currencies corresponding to the 4country equity indexes in your portfolio. For your portfolio, calculate the optimal foreign exchange hedging positions (i.e., portfolio weights) using spot FX rates. You cannot use Hong Kong in this calculation because it has almost a fixed exchange rate with the USD.Also, the original Euroland countries now have a common FX rate. I have linked this backward using the Deutsche Mark prior to 1999. Simply add the currency returns in dollars to the index returns in dollars for your portfolio allocation problem.[/list]
[/list]

iixmm 2019-1-27 05:51 PM

[quote]原帖由 [i]落漠笨拙的樹根[/i] 於 2019-1-24 11:20 PM 發表 [url=https://www.discuss.com.hk/redirect.php?goto=findpost&pid=493922878&ptid=27994628][img]https://www.discuss.com.hk/images/common/back.gif[/img][/url]

The Excel spreadsheet for the case contains:
Monthly stock price indexes denominated in local c ... [/quote]
CityU?