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Transcript
Chapter 6
Efficient
Diversification
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%
Easy
6-2
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
6-3
Summary: Portfolio Risk/Return
Two Security Portfolio
• Amount of risk reduction depends critically
or covariances
on correlations
_________________________.
<1
• 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)?
6-4
Extending Concepts to All
Securities
• 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
6-5
6.3 The Optimal Risky Portfolio With A
Risk-Free Asset
6.4 Efficient Diversification With Many
Risky Assets
6-6
Including Riskless Investments
• The optimal combination becomes linear
• A single combination of risky and riskless
assets will dominate
6-7
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
6-8
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.
6-9
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
systematic.
• That is, the variation in returns of a well
diversified portfolio must be due to changes in
systematic factors
• Tremendous computational advantage makes it
practical!
6-10
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
6-11
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
6-12
6.6 Risk of Long-Term Investments
Are Stock Returns Less Risky in the
Long Run?
6-13