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B9339 Homework Assignment

创建日期：2024-07-01 15:51:51

所属分类：计算机computer science

标签： B9339

Homework Assignment

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B9339 Homework Assignment

1. (Sharpe ratio enhancement) In this problem, you are to investigate conditions under which
additional investment strategies are beneficial to an existing portfolio. Suppose that you
already have a portfolio and that you are considering adding n new strategies to it. Your goal
is to improve your existing portfolio, and you expect the new strategies to be “beneficial.” A
natural question that arises in this situation is what is the “relationship” between your
existing portfolio and the new strategies that is necessary so that the addition of the new n
strategies is beneficial for your existing portfolio.
To approach this question, you make the following simplifying assumptions:
(a) Your notion (criterion) of “beneficial to your portfolio” amounts to increasing the Sharpe
ratio (defined as the ratio of return over volatility) of your existing portfolio, SRold;
(b) You can adequately describe the correlation structure of the new n strategies by a single
parameter, their average pairwise correlation ρnew;
(c) You can adequately describe the correlation structure of your existing portfolio and the
new n strategies by a single parameter, the average correlation ρold,new of all the pairwise
correlations between your existing portfolio and each of the new strategies;
(d) All the new strategies you are thinking of adding have equal Sharpe ratios, SRnew;
(e) Your portfolio allocation ensures that in your portfolios (existing and new), each
component (strategy) contributes an equal amount of 1 unit of marginal volatility (i.e., in
your new portfolio, your existing portfolio would be contributing an equal amount of
volatility as each of the new strategies).
With this framework:
1. Explain how you can achieve the portfolio allocation of assumption (e) above.
2. Derive an upper bound for the parameter ρold,new in terms of SRold, n, ρnew, SRnew , so
that your new portfolio is indeed an improvement over your existing portfolio.
3. When you are adding only one strategy (n=1), what does your bound in (i) reduce to?
4. Plot your bound for n=1, as a function of SRnew for the typical values of strategy Sharpe
ratios we have seen so far: SRold = 0.25, 0.50, 0.75, 1.00, 1.25. Explain why your plots
make/do not make intuitive sense.
Explain how much more complicated your analysis (bound) becomes if, keeping all other
assumptions intact:
5. All the new strategies do not have the same Sharpe ratio as in assumption (d) above.
6. You cannot adequately describe the correlation structure of your existing portfolio
and the new n strategies by a single parameter as in assumption (c) above.
7. You cannot adequately describe the correlation structure of the new n strategies by a
single parameter as in assumption (b) above.
8. Give an example of another notion (criterion) for “beneficial to your portfolio” that is
different from the Sharpe ratio assumed in assumption (a) above. Explain the
rationale behind your alternative criterion, and how it differs from the Sharpe ratio.
Outline how you could approach the question of the problem for your alternative
criterion (only a brief description is needed; you do not need to carry out the analysis).

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关键词一关键词二关键词三关键词四关键词五和法规和的发更好的风格和 ECON 615 FINC 612 CSC148 COMP 639 ACCT 203 ACCT 211 PSYC 101 MTH2009 COMP52315 PSYCO 432 statistics MATH4063 11 xxx 1 MA1MSP MAST30028 MATH3888 CS341 EEE30002 ES2F5 MCD4160 CC0933 ECON 1101 MCHM3001 CHEM3118 COMMGMT 2511 COMP41280 STAT 631 24T1 IRE379 SENG365 ECON433 FIT3139 MATH4602 LING5621M FINS5516 ECON3208 MN2177 L2 SM EEET1415 Finance DS4023 COMP3004 7CCSMRTS K1S5B6 Stat230 CSCI4211 CSI2132 ECON30130 MAS6100 ENVS222 COM2107 INFO1112 STAT 4004 FIT2100 comp2022 COMP4691 Physics 307 Econ 659 probability CSCI316 fir29 CSCI203 COMP3160 COMP6714 INFO1113 Physics 7B Physics Photonics S203031 STAT2005 COMP90015 CSCI 2110 CSCC46 Information CSC477 COMP4650 Statistical COMP 346 COMP1017 ELEC340 MATH1007 Programming function STAT 244 CS 134 Java cse13s Math 108A FW20 ECON3389 CSE 130 Science 331 COMP9020 engineering COSC 445 CSE 5523 GAME2012 visualization MATH 235 Math 370 CSC343 COGS 108 EE524 COMP10200 STAT 416 3FK4 MSCI 311 ECON6113 ACC40700 EMESTER1 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