Portfolio Management Grenoble Ecole de Management MSc Finance Fall 2009

Risk is not a vague concept The convention is to define risk as the variance of returns. 2 with

Risk is not a vague concept The standard deviation which is the square root of the variance is easier to interpret because it has the same dimension as returns 3 Standard-error is also referred as volatility

Covariance as a measure of diversification 4

Beta one of the most important idea of this course: the risk of a well-diversified portfolio depends on the sensitivity to market risk (beta) of the securities included in the portfolio not of the unique risk of each security in the portfolio If we want to know the contribution of an individual security to the risk of a well diversified portfolio, it is no good thinking about how risky that security is if held in isolation. We need to measure its sensitivity to market risk, market movements. That is because unique risk can be eliminated by diversification. This sensitivity is called Beta. 5

Betas and covariances A statistician would define the beta of stock i as: 6

Efficient Portfolios – 2 assets 7 Portfolios which dominates are said to be efficient. The location of these portfolios is the efficient frontier or minimum variance frontier. It runs from the global minimum variance portfolio (70% Energy – 30% Materials) to the farthest on the right. Variance Expected Returns

Lending and Borrowing 8 Since borrowing is negative lending we can extend the range of possibilities to the right of the market portfolio

Capital allocation line 9 The capital allocation line describes the combinations of expected return and standard deviation of return available to an investor from combining her optimal portfolio of risky assets with the risk free asset. The CAL is the line starting at the risk free rate of return that is tangent to the efficient frontier of risky assets.

Capital Asset Pricing Model 10 The use of the CAPM simplifies the estimation of the variance- covariance matrix. It has further implications: it is a single factor equation describing the expected return on any asset as a linear function of its beta. Security market line: the relation between risk and returns for any asset 1 i

CAPM: in practice 11 The β representation of the investment universe: greatly reduce the computational task of providing the inputs to a mean-variance optimization. enables one to rank assets according to their sensitivity to market (systemic) risk. enables one to estimate expected return for any asset knowing the risk-free rate, R f, and the market risk premium enables one to measure the marginal risk contribution of an asset to an index or a portfolio

Sector weighting-Stock selection. 12 The preceding equation can be rearranged to form the following relationship: 1 is pure sector allocation. It assumes that within each sector the manager held the same securities as the benchmark and in the same proportions. 2 is allocation/selection interaction. Joint effect of the portfolio managers’ and security analysts’ decisions to assign weights to both sectors and individual securities. It equals the difference between the weight of the portfolio in a given sector and the portfolio’s benchmark for that sector, times the difference between the portfolio’s and the benchmarks returns in that sector, summed across all sectors.

Sector weighting-Stock selection is within sector selection. return implicitly assumes that the manager weights each sector in the portfolio in the same proportion as in the overall benchmark, although within the sector the manager may hold securities in different from benchmark weights. Thus, the impact on relative performance is now attributed only to the security selection decisions of the manager.

Ex post alpha 14 The level of skills depends on the sign and value of alpha which measures the vertical distance to the SML. We seek managers with positive alpha: managers that have excess returns compared to the risk of their portfolios.

Balanced portfolio 15 WeightsBetaBeta P Sector A3%0,70,021 Sector B2%0,90,018 Country 14%1,30,052 Country 22%1,70,034 Country 36%0,80,048 Small Cap11%1,60,176 Value stocks12%1,10,132 Index ETF10%10,1 Future Index-15%1-0,15 Option Index-4,3%1-0,043 Total50% 0,39 WeightsSensitivitySensit P Euro 2Y25%1,70,425 EURO 10Y10%70,7 Euro 30Y2,5%160,4 Cash10,5%00 Margin2%00 3-month Fw 1,4 EUR IR-3% 00 US IR3% 00 Total50% 1,53 Overlay/alternative L/S Small Cap20%1,60,32 Large Cap-20%0,9-0,18 Portable alpha Fund HugeReturns10%1,30,13 Future Index-10%1-0,1 Etc… Total Equity50% 0,56 Weights are useless, only risk measure must be used: betas, duration, credit risk…