Alpha Holdings appoint you as their junior quant analyst. The CIO is interested to knowing how the S&P 500 market

index is affecting energy stock such as Schlumberger (NYSE: SLB).

Schlumberger NV engages in the provision of technology for reservoir characterization, drilling, production and

processing to the oil and gas industry. It operates through the following business segments: Digital and Integration,

Reservoir Performance, Well Construction, and Production Systems. The Digital and Integration segment combines the

company's software and seismic businesses with its integrated offering of asset performance solutions. The Reservoir

Performance segment consists of reservoir-centric technologies and services that are critical to optimizing reservoir

productivity and performance. The Well Construction segment includes the full portfolio of products and services to

optimize well placement and performance, maximize drilling efficiency, and improve v. Ilbore assurance. The

Production Systems segment develops technologies and provides expertise that enhance production and recovery

from subsurface reservoirs to the surface, into pipelines, and to refineries. The company was founded by Conrad

Schlumberger and Marcel Schlumberger in 1926 and is headquartered in Houston, TX.

The S&P500 market index is used as a good representation of the U.S. equity market. Yearly returns data is used, and

the single index model results are as follows:

SLB

S&P 500

31-Dec-21

47.65%

36.50%

31-Dec-20

6.66%

31-Dec-19

13.47%

31-Dec-18

-43.76%

-1.53%

Average risk

46.96%

18.51%

Average return

-8.21%

18.22%

Coefficients

Alpha

-0.5237

Beta

2.4232

Given a standard deviation of the error of

0.1388

(a) If the S&P500 market index is expected to change from 4900 to 4200, what is the expected return on SLB? Show

your workings. (1 mark)

(b) Provide some clear justifications why you would use the single index model over the Markowitz model in

determining the variables required to construct a client's portfolio made up of 65 stocks? [2 marks]

(c) Estimate SLB's total risk (standard deviation) using the Single Index Model. [2 marks]

(d) Evaluate the impact of SLB's market risk in calculating the stock's variance. [2marks]

(e) You are looking into the construction of a portfolio, which will be made up of two stocks, namely SLB and Billabong

(Ticker: BBG). Given the beta of BBG is 0.97, and the standard deviation of BBG is 25%, calculate the correlation

coefficient between the two stocks. [2 marks]

(f) If you must decide between creating a portfolio made up of SLB and BBG based on the results in (d), and a

portfolio made up of SLB and Yahoo which has a correlation coefficient of -0.325, which one would you recommend?

Explain your answer. [2 marks]

If you want to construct a portfolio based on 10% SLB, 35% Billabong and the rest invested in a risk-free asset,

what would be the portfolio beta? Show your workings. [1.5 marks]