# Long-Short Portfolio Strategy

Updated: Nov 12, 2017

# The Purpose of this project was to form a portfolio by assessing risk metrics for a set of stocks. We calculated different portfolio strategies to find the most optimal risk and performance measurements. These metrics signal powerful meanings to investors, but cannot solely be used to judge an investment. This project serves as an introduction to how these quantitative signals can convey copious amounts of information and affect or everyday decision-making.

Introduction

For this project, we assumed the role as a portfolio manager and were tasked with identifying 14 publicly traded companies to collect information on. Our universe, comprised of 14 companies, was selected using Yahoo Finance in conjunction with further industry research. Each of the firms were measured using various risk performance metrics including: arithmetic and geometric returns, standard deviation of return, beta relative to the market, idiosyncratic volatility, Share ratio, Jensen’s alpha and four-factor alpha. The selected companies were benchmarked against the S&P 500.

We created tree portfolios: a long-only portfolio, a short-only portfolio, and a long-short portfolio. These portfolios were built based off of the firms Sharpe Ratio in comparison to the other companies we selected. The top four Sharpe Ratios were added to our Long Portfolio, whereas the four firms with the lowest Sharpe Ratio’s were shorted.

**Risk-adjusting Returns**

__Sharpe Ratio__

The Sharpe ratio is a way to look at an investment by seeing how well the return of an asset is doing with compensating an individual for the risk taken in the investment. The goal for the investor is to be able to analyze how well their return is in relation to the risk that was taken in investment and determine if the asset is worth adding or keeping in a portfolio.

At the numerator, it takes the expected portfolio return minus the risk-free rate. It then divides it by the standard deviation of the portfolio, which is in the denominator. There are several reasons why the Sharpe ratio is useful. One way to utilize the ratio is with the comparison of two assets against a common benchmark and then can notice that the one with the higher Sharpe ratio provides a greater return for the risk of the investment. The ratio can also be used to compare any change in a portfolio’s risk/returns when a new asset is added to portfolio

“We created tree portfolios: a long-only portfolio, a short-only portfolio, and a long-short portfolio. These portfolios were built based off of the firms Sharpe Ratio in comparison to the other companies we selected. The top four Sharpe Ratios were added to our Long Portfolio, whereas the four firms with the lowest Sharpe Ratio’s were shorted.”

A positive alpha indicates the portfolio manager performed better than expected considering the risk the manager assumed with his investment decisions. On the other hand, a negative alpha indicates the portfolio manager underperformed relative to the risk the manager took. In other words, it measures the performance of a portfolio manager relative to the risk he/she assumes.

Calculations

__Raw Data__

Returns = (new price-old price) -1

1+Returns = 1 + Return% in the row

Return-Rf = Return Cell - Corresponding rf cell in the same row

__Long Port & Short Port__

Sharpe Ratio = Mean monthly arith returns/std. Deviation of return

Mean Monthly Arith. Returns = Average (All cells in Ret-RF)

Mean Monthly Geom Returns = GEOMEAN(All Cells in 1+Return)

Std. Deviation of Return = STDEV(All cells in Ret-RF)

Beta Relative to the Mkt = SLOPE(All cells in Ret-RF,All cells in Mkt-RF)

__L-S Port__

Ret - RF= Long Port - Short Port in same row

1+ Return = 1 + (Long Port-Short Port in same row)

__Linear____ ____Regression__

Using Excel Data Analysis

__CAPM Alpha__

CAPM Alpha is often considered to represent the market’s movement as a whole or the active return on an investment that measures and compares the performance of an investment against market index. The excess returns of the investment or portfolio of investments compared to this benchmark is the investment or portfolio alpha.

The equation for alpha is expressed as:

α = Rp – [Rf + (Rm – Rf) β]

A positive alpha indicates the portfolio manager performed better than expected considering the risk the manager assumed with his investment decisions. On the other hand, a negative alpha indicates the portfolio manager underperformed relative to the risk the manager took. In other words, it measures the performance of a portfolio manager relative to the risk he/she assumes.

__Excel Calculations__

__Beta__

To calculate Beta in excel we used the SLOPE() function. We also ran a linear regression and analyzed the slope coefficient using Data Analysis.

__Fama-French Four-Factor Model__

The four factors in the model are the Market risk free rate, SMB, HML, and Momentum. Small minus big (SMB) is the return of a pure long-short portfolio, long a broad portfolio of small cap stoks. HML (High Minus Low) is the return of a pure long-shore portfolio, long a broad portfolio of high book-to-price (B/P) stocks, and short a broad portfolio with a low B/P.

We chose a sample period and frequency of monthly returns over the last 10 years for each of the 14 stocks. For each stock we had 121 monthly excess returns. Then for each stock I ran a linear regression. The factor betas became the slope coefficient and the stock’s Idiosyncratic Variance was the square of the regressions standard error. After that we put the Factor Betas in a diagonal matrix and calculated the covariance.

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