Project objective

The objective of the project is to construct a low-volatility portfolio, assess its risk and return structure, as well as its performance.

Data

The data is contained in "Project_Data.xlsx". In the data set are prices of 10 assets, which include a fund that mimics the benchmark S&P 500 Index (ASSET 1).  The time series are from June 30, 2006 to December 31, 2009.

Construction of a low-volatility portfolio

The first exercise is the construction of an equally-weighted low-volatility portfolio, using ASSET 2 to ASSET 10.

Assume an initial capital of $1,000,000, with the portfolio being long only (i.e., no short positions can be taken).

The initial formation of the portfolio is set on June 30, 2007, by screening for low-volatility assets which are then used to construct an equally-weighted low-volatility portfolio. (Note: Low- volatility assets are those with past one-year down-market betas of less than or equal to one. See below for more details on the dual-beta model.)

Six months later, on December 31, 2007, the portfolio is to be rebalanced, using the aforementioned process. Continue with this six-month rebalancing procedure until the data has been exhausted.

Assessment of the low-volatility portfolio

As for the second part of this project, the equally-weighted low-volatility portfolio is then analyzed over the period June 30, 2007 to December 31, 2009. The benchmarks against which the portfolio is assessed against is ASSET 1 and an equally-weighted portfolio across the other nine assets (that is, ASSET 2 to ASSET 10), which is rebalanced on the same dates as the low- volatility portfolio.

First, assess the low-volatility portfolio and benchmarks' risk and return structure.

Second, assess the performance of the low-volatility portfolio and benchmarks by employing the Fama-French (1992) and Carhart (1997) four-factor model, with data provided by Professor Kenneth French.1 The relevant data are "Fama/French 3 Factors [Daily]" and "Momentum Factor (Mom) [Daily]".

(Note: The Fama-French-Carhart four-factor model is an industry standard when it comes to assessing investment performance and its methodology is made widely available on the Internet.)

THE DUAL-BETA MODEL

The dual-beta model is an extension of the standard Capital Asset Pricing Model (CAPM). It estimates separately the parameters for up-market, when the daily return for the market index is non-negative, and down-market, when the daily return for the market index is negative. The dual-beta model can thus be expressed as

(r_j - r_f)_t = α_j⁺D + β_j⁺ (r_m+ - r_f)_t D + α_j^- (1 - D) + β_j^- (r_m^- - r_f)_t (1 - D) + ε_t,

where α_j⁺ , β_j⁺, α_j^-, and β_j^-  are the estimated parameters for up-market and down-market days respectively; r_m⁺ = r_m on days the market index did not decline and  r_m^- =  r_m on days it did; D is a dummy variable, which takes the value of 1 when the market index daily return is non- negative, and zero otherwise. If there is no asymmetry in beta, then the dual-beta model is identical to the standard CAPM model.

Attachment:- Project_Data.xlsx