Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: THEend8_
ECM9/ECM10/ECM11
MPhil in Economics
MPhil in Economic Research
MPhil in Finance and Economics
TOPICS IN APPLIED ASSET MANAGEMENT
Candidates are required to answer two compulsory questions
Write your candidate number (not your name) on the cover of the Project.
1 of 6
Questions 1 is weighted at 25%, Question 2 is weighted at 75%
The answer should be no longer than 3000 words inclusive of footnotes and
appendices but exclusive of bibliography
One A4 Page consisting largely of charts, statistics or symbols will be
regarded as the same as 250 words (pro rata for less than A4 page)
F540 : Topics in Applied Asset
Management
Assessment / Project 2021
Answer both questions; 25% of the final mark will come from the theoretical
question 1 and 75% will come from the empirical exercise- question 2 .
THEORETICAL EXERCISE
1. Factor Risk Budgeting additively decomposes individual asset or portfolio re-
turn risk measures into factor contributions allowing a portfolio manager to
know the sources of factor risk for allocation and hedging purposes and allows
a risk manager to evaluate a portfolio from a factor risk perspective. Assume
an asset or portfolio return Rt can be explained by a factor model (FM), with
k factors, of the form
Rt = α + β
′ft + t
where ft ∼ iid(µf ,Ωf ), t ∼ iid(0, σ2 ), cov(fk,t, s) = 0 ∀ k, t, s . Rewrite the
factor model as
Rt = α + β
′ft + t = α + β′ft + σ × zt
=α + β˜′f˜t
β˜ = (β′, σ)′, f˜t = (ft, zt)′, zt =
t
σ
∼ iid(0, 1)
then
σ2FM = β˜
′Ωf˜ β˜, whereΩf˜ =
(
Ωf 0
0 1
)
denoting the risk measure σFM (the factor model vol) by RM(β˜) show
(a) RM(β˜) is a linearly homogeneous function of β˜
(b) Apply Euler’s theorem to provide an expansion of RM(β˜) into k , β com-
ponents and an asset/portfolio specific risk factor
(c) find simple expressions for an individual factor j’s marginal contribution
to risk, then factor j’s contribution to risk and finally for each factor,
j = 1, ...., k, expressions for their percent contribution to risk and the
asset/portfolio specific factor contribution to risk, ie. j = k + 1
2 of 6
(d) Show the same analysis can be applied for Portfolio Risk Budgeting when
you can additively decompose portfolio risk measures into asset contribu-
tions which allows a risk manager to evaluate a portfolio from asset risk
perspective; ie. with a portfolio return
Rp,t = w
′Rt =
N∑
i=1
wiRit
and let RM(w) denote the portfolio vol, σp. The same analysis can in fact
be applied to any convex risk measure in place of vol, such as Value at
Risk and Expected Shortfall. You may wish to use this analysis in your
empirical exercise.
(e) Consider an investment universe of N assets with R = (R1, ..., RN)
′ ∼
N(µ,Σ) and a portfolio with weights x = (x1, ..., xN)
′ and
∑N
i=1 xi = 1
i. Derive the relationship between the β of the portfolio against a bench-
mark or market portfolio and the βi of the individual assets
ii. Given a quadratic utility function- verify that the optimal portfolio is
a linear function of the risk premium and derive an explicit expression
for the implied risk premium,pi = µ− r where r is the risk free rate.
iii. The investor assumes an ex-ante Sharpe Ratio for their portfolio,
SR(x|r) where r is the risk free rate. Show the risk aversion parameter
φ then satisfies the following relationship
φ =
SR(x|r)√
x′Σx
iv. Deduce then that the implied risk premium of asset i is a linear func-
tion of its marginal volatility.
v. What is the economic interpretation of this previous relationship
vi. Find a new expression of the Sharpe Ratio in terms of marginal volatil-
ities.
EMPIRICAL EXERCISE
The empirical exercise is based on developing strategies that seek to be robust
to different phases of the market or the global macro-economy i.e. “disaster proof”
or defensive strategies and hence factor timing, tilting or style rotation are the
issues to explore. You are free to follow your own path in the project as long as
you demonstrate knowledge of the material and techniques that have been covered
in the course.
3 of 6
The steps outlined below should be covered and developing these beyond that
indicated below would increase the final grade awarded. While the more demand-
ing choices that you may make in your empirical analysis will gain greater credit
you must start simple and only attempt more advanced methods if you have al-
ready completed a basic analysis as far as step(e) for instance below, have the time
and are confident in the potential to deliver further results. Be careful to prevent
look ahead bias in your computations - do not let your strategies use data that
would not have been available at the time of strategy deployment- use suitable
lagged inputs and rolling windows for building and implementing your strategies.
1. A section on the course Moodle site has been set up to help you download
your data from CRSP but you may want to get data from other sources. The
development of your data base is your own responsibility but start by down-
loading stock price for the 100 random stocks (PERMNOs) allocated to you
from CRSP for the longest period you can with a common sample size with
no NAs. You can also if you wish download a subset of associated set of stock
characteristics (fundamentals) which will necessarily be for a shorter period-
see the data note on Moodle, a risk free rate, S&P500 index as well as data
on factors of your choice from a variety of sources that will probably include
Ken French’s and/or AQR’s web site, volatility factors can also be found on
Robeco’s web site . If you
want to use ETF’s they can be downloaded from CRSP- notice in particular
a number of potential hedge ETFs- Bonds, defensive sector indices etc.- again
feel free to expand on this set of data as you wish- for instance you could
also decide to construct technical indicators along the lines of the Neely et al
paper we considered in the lectures. For constructing technical indicators see
the bookdown book Technical Analysis in R by Chiu Yu Ko and R packages
Quantmod, Quantstrat or TTR. Equally you will most probably want to con-
sider ie. construct or download various “risk alarms” such as VIX or use macro
signals from the FRED web site. Your empirical work will be carried out on a
monthly basis. Locate periods of macroeconomic recession and market- “good”
and “bad” periods- crisis, expansion or downturn in your sample possibly using
the NBER indicators. Build your data set.
(a) Diversification: Examine the diversification of your universe of assets to be
considered for inclusion in your portfolio and from these select an investible
and well diversified set with consideration of the objective of building a
defensive strategy. Consider how this set may have changed through time
by exploring diversification over relevant sub periods using tools covered
in the course in a rolling window manner. Comment on what you find.
(b) Return Prediction:Next consider several different approaches to forming