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Chapter 6
Two-Security Portfolio Return
E(rp) = W1r1 + W2r2
W1 = 0.6
Wi = % of total money
W2 = 0.4
invested in security i
r1 = 9.28%
r2 = 11.97%
E(rp) = 0.6(9.28%) + 0.4(11.97%) = 10.36%
Portfolio Variance and Standard
Deviation: Hard!
Consider something simple first instead
 is always in the range __________ inclusive.
Consider 1, 0, -1 benchmarks, ranges in between
Which value is ideal for diversification? (use logic,
or math formula of portfolio variance in your book)
• Again Chapter 11 in FINC301
Summary: Portfolio Risk/Return
Two Security Portfolio
• Amount of risk reduction depends critically
or covariances
on correlations
• Adding securities with correlations _____
will result in risk reduction.
• If risk is reduced by more than expected
return, what happens to the return per unit
of risk (the Sharpe ratio)?
Extending Concepts to All
• Consider all possible combinations of securities,
with all possible different weightings and keep
track of combinations that provide more return
for less risk or the least risk for a given level of
return and graph the result.
• The set of portfolios that provide the optimal
trade-offs are described as the efficient frontier.
• The efficient frontier portfolios are dominant or
the best diversified possible combinations.
All investors should want a portfolio on the
efficient frontier. … Until we add the
riskless asset
6.3 The Optimal Risky Portfolio With A
Risk-Free Asset
6.4 Efficient Diversification With Many
Risky Assets
Including Riskless Investments
• The optimal combination becomes linear
• A single combination of risky and riskless
assets will dominate
Dominant CAL with a Risk-Free
Investment (F)
• CAL(P) = Capital Market Line or CML dominates
other lines because it has the the largest slope
• Slope = (E(rp) - rf) / sp
(CML maximizes the slope or the return per unit of risk
or it equivalently maximizes the Sharpe ratio)
• Regardless of risk preferences some
combinations of P & F dominate
Practical Implications
o The analyst or planner should identify what they
believe will be the best performing well
diversified portfolio, call it P.
P may include funds, stocks, bonds, international and
other alternative investments.
o This portfolio will serve as the starting point for all
their clients.
o The planner will then change the asset allocation
between the risky portfolio and “near cash”
investments according to risk tolerance of client.
o The risky portfolio P may have to be adjusted for
individual clients for tax and liquidity concerns if
relevant and for the client’s opinions.
6.5 A Single Index Model: CAPM
• Systematic risk arises from events that effect the
entire economy such as a change in interest
rates or GDP or a financial crisis such as
occurred in 2007and 2008.
• If a well diversified portfolio has no unsystematic
risk then any risk that remains must be
• That is, the variation in returns of a well
diversified portfolio must be due to changes in
systematic factors
• Tremendous computational advantage makes it
Sharpe Ratios and alphas
• When ranking portfolios and security performance
we must consider both return & risk
• “Well performing” diversified portfolios provide
high Sharpe ratios:
– Sharpe = (rp – rf) / sp
• You can also use the Sharpe ratio to evaluate an
individual stock if the investor does not diversify
Sharpe Ratios and alphas
“Well performing” individual stocks held in
diversified portfolios can be evaluated by the
stock’s alpha in relation to the stock’s
unsystematic risk.
Seeking Positive Alphas
6.6 Risk of Long-Term Investments
Are Stock Returns Less Risky in the
Long Run?