Optimal risky portfolio formula

You have been assigned to construct the optimal portfolio comprising two risky assets (Portfolios A & B) while considering the client’s risk tolerance. The attached spread sheet shows historical monthly returns of the two portfolios, the S&P 500 and 90-day Treasury Bills. Also shown are the annualized returns for each for the period specified.

1.The first risky asset (Portfolio A) is a US equity strategy that uses publically available valuation, technical and sentiment factors to assess which stocks are over-priced and which are under-priced. Fundamental factors indicate the magnitude and quality of a company’s earnings and the strength of its balance sheet. Examples of such factors include: cash flow growth, cash flow return on invested capital, price to cash flow, and accruals which assess earnings quality (low quality earnings indicate that management may be manipulating earnings by adjusting accruals). Companies with favorable fundamental factors tend to outperform those with less favorable factors.

2.Technical and sentiment factors seek to identify mis-pricings resulting from investor behavior. Examples include: momentum and price reversals where investors tend to over-react to good news by bidding up prices ABOVE fair value and bad news by bidding down prices BELOW fair value; short interest on a stock which can indicate the investor sentiment about the company’s prospects; share buybacks which can indicate a positive signal from management’s optimism regarding a firm’s future prospects; and earnings / revenue surprise. Firms with favorable technical and sentiment factors also tend to outperform. For example, firms whose earnings and revenue exceed analysts’ expectations tend to continue to outperform vs. those firms that experience earnings surprise due to cost cutting.

3.Starting with the market portfolio, the US equity strategy over-weights those stocks with more favorable fundamental, technical and sentiment factors and under-weights or avoids those stocks with less-favorable or un-favorable factors. The strategy seeks to out-perform the market portfolio as represented by the S&P 500. The monthly returns of the US equity strategy are shown in the attached spreadsheet (Portfolio A).

4.The second risky asset (Portfolio B) is a global macro hedge fund. This strategy seeks to benefit from mis-pricings within and across broad asset classes by taking long and short positions in equity markets, bond markets and currencies. For example, if the manager believes that US equities will out-perform Japanese equities, the portfolio will go long S&P 500 futures and short TOPIX futures (TOPIX is a Japanese equity index). This long/short trade is not impacted by the overall direction of global equities, but rather the relative movement between US and Japanese equities. Similarly for bonds, if the manager believes that interest rates in the United Kingdom (UK) will decline more so than interest rates in Australia, then the manager will buy UK gilt futures (gilt is the 10-year UK bond) and short Australian 10-year bond futures. Again, this trade is not impacted by the overall direction of global interest rates, but rather the relative movement between UK and Australian rates. Recall that bond prices rise as interest rates decline. The global macro hedge fund is mostly market neutral meaning that long positions equal short positions thereby dramatically reducing systematic exposure (low beta).