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The Sharpe’s Way to Minimum Variance Portfolio (Case Study – Sharpe Portfolio Optimization)

~~~ Beginning of the Case ~~~
The Sharpe’s Way to Minimum Variance Portfolio
(Case Study – Sharpe Portfolio Optimization)

With the mixed feeling of fear and excitement, Jyoti entered her name in the visitor entry register, and in the column for person to visit, he wrote Mr. Sunil Naik and purpose of visit as New Joinee. Jyoti Kapur, who recently completed her Post-graduation in Finance from a reputed B-School had been handpicked during campus interview by Mr. Sunil Naik, a CFA and a well-known and experienced Buy-Side analyst, specializing in equity portfolios for Very High New Worth Clients. Delite Consulting was a global brand known for financial services, mostly on the auditing side, also have established a division in India to service global fund managers, in advising and managing portfolios of equity stocks. Sunil had been highly impressed with Jyoti’s resume, especially her credentials in the additional projects section, where she had mentioned about her attempts at equity analysis and portfolio management. She had mentioned about her hands-on experience in financial modelling to build optimum portfolios that generate adequate return while minimizing the risk. He had asked her during the interview about the same, and she had told him, that she had written research articles and also worked in a boutique share broking firm during her summer internship, where she had used William Sharpe’s Single Index Model to build the minimum variance portfolio. Sunil believed in recruiting his Assistant Analysts fresh out of college, but with a contextual understanding of markets and portfolio building process, for it makes his life easier, yet allows him to extract fresh ideas.
The first few days of Jyoti at Delite was about getting oriented about HR policies, getting to know people, processes and systems. She was made to attend meetings with Sunil. Sunil’s team had a bunch of young enthusiastic analysts, who were very cooperative to Jyoti in getting her settled down. Jyoti would meet the team once in a week and today was supposed to be the first such team huddle, Jyoti is going to be part. She was told, she would be given her first assignment in the meeting by her team mates.
“So, Ms. Jyoti, how is Delite treating you…?”, asked Sunil looking at Jyoti. They were in the meeting hall with other team mates for their weekly huddle. Jyoti, with a smile on her face said – “Very well sir. People here are so nice and cooperative. I must tell you sir, Delite for sure has an excellent work culture. I am looking forward for being part of assignments to work with the team.” Pulling out a set of printed out sheets, which looked like some random report with some tables that contained some financial numbers, Sunil gave a controlled smile. Handing them over to Jyoti, he spoke – “Good to know Jyoti. That you found the workplace comfortable. Yes. We do intend to create a culture that makes it easier for individuals to excel. Hoping to see you shine. Coming to your first assignment, yes, I do have this for you. This is a partially done report by one of our former employee. By the way, this project belongs to a very high net worth client in New York, who is routed to us through our partner firm in US. This client wants us to create a portfolio for him for a fairly long-term horizon and I guess his need is to create a special fund. Go through these. Try to come out with a simple initial report and a portfolio. I will introduce you to the client by tomorrow by 10 am EST. We will do the webcon from my office. You can take support from team here. Go ahead”. Jyoti was already thinking of her project that she had done during her college days. She had used Sharpe’s Single Index Model to create a minimum variance portfolio. She was trying to recall, where she had saved that spreadsheet model she had created.
Back at her desk, she browsed through the documents given by Sunil. She found that this client Mr. Kunal Mishra, a green card holder in US, is a big time investor in NASDAQ. He had placed this special request for a legacy fund creation with approximately eight year time horizon. This information was available in the Investment Policy Statement created by the first analyst. Jyoti knew that before processing for any advisory, Delite arranges for a detailed discussion with client with the assigned portfolio manager, to understand the client’s investment objectives, constraints, preferences, risk taking ability and the evaluation requirement. Jyoti understood that this client wants this portfolio to be less speculative and as lower risky as possible, while not compromising on returns as much as possible. His intention was to start the portfolio with an investment of US$ 6 million She also found a partially completed table, where a list of stocks were shortlisted by the previous manager, and supposedly, agreed upon by the client as well. The table is given below:

Jyoti also collected the below information from her colleagues regarding various market rates used by Delite, in such portfolio construction processes:

If you were Jyoti, how would you go about constructing the portfolio? Prepare a one page report that can be shared with the client highlighting the list of stocks and the investible amount in each stock. Also explain in non-technical terms, by following this particular process, what is the client achieving.
(Hint: Use Sharpe’s Single Index Model & Use Spreadsheet Modeling )
~~~ End of the Case ~~~
(I)                 E J Milton, M J gruber and M W Padberg, “ Optimum Portfolios from Simple Ranking Devices”, Journal of Portfolio Management (1978)
(II)               Chapter 18, Security Analysis and Portfolio Management by Donald E. Fischer and Ronal J. Jordan

I.                   What courses are intended to be using this case?
This case can be used as part of finance course like Financial Management, Security Analysis and Portfolio Management, Financial Modelling/Analytics/Engineering, Quantitative Finance Investment Management, Equity Research and Wealth Management.
II.                What concepts/models/theories can be explained using this case?
This case can be used to demonstrate the below concepts/theories/models/applications:
(a)    Risk and Return of Portfolios
(b)    CAPM and Sharpe’s Theories
(c)    Markowitz’s Modern Portfolio Theory
(d)    Quantitative Benefits of Diversification
(e)    Concepts of systematic, unsystematic and total risk
(f)     Portfolio Construction
(g)    Minimum Variance Portfolio
III.             What main issue/problem/dilemma is addressed in this case?
The case addresses the problem of identifying the exact amount of investment to be made in selected stocks, such that the excess-return-to-systemic-risk ratio is maximized.
IV.             Teaching Notes:
Write to for detailed teaching notes.