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AD 717:
Investment Analysis and
Portfolio Management
John McLaughlin, CFA, FRM
mclaugh3@bu.edu
Measuring Firm Performance
ROA = Operating Income / Assets
ROE = Net Income / Shareholder’s Equity
ROC = NOPAT / (Debt + Equity – Cash)
Beyond Financial Analysis
Business Risk
Financial Risk
Quantitative Analysis
• Macroeconomic Factors
• Market Share & Composition
Productivity
• Absolute
• Trend
• Comparisons
Qualitative Analysis
•
•
•
•
• Financial Policy
• Accounting Policy
• Financial Flexibility
Competition
Regulation
Management
Governance
Qualitative items are often ambiguous, more difficult to discern and judgments about them
inherently subjective:
•
•
•
Just how good is the management team?
How does their strategy stack up against its
•
competitors?
How fierce or relaxed is the competition in that sector? •
What are the growth prospects for that product or
sector?
Will new regulation go into effect and what will be its
impact?
How good is the accounting disclosure?
Beyond Financial Analysis
Macroeconomics and Industry Analysis
• Intrinsic value if a company comes from its earnings prospects
determined by:
• The global economic environment
• Economic factors affecting the firm’s industry
• The position of the firm within its industry
Macroeconomics and Industry Analysis
Atech has fixed costs of $13.0 million and profits of $5.0 million. Its competitor,
ZTech, is roughly the same size and this year earned the same profits, $5.0 million.
However, ZTech operates with fixed costs of $7.0 million.
• Calculate the operating leverage for each firm.
DOL𝐴𝑇𝑒𝑐ℎ = 1 +
Fixed Cost
$13,000
$7,000
=1+
= 3.60 & DOL𝑍𝑇𝑒𝑐ℎ = 1 +
= 2.40
Profit
$5,000
$5,000
• Which firm will have higher profits if the economy strengthens?
• For that, we have to know more about the variable costs!
• If they are comparable, then ATech because of their higher operating leverage!
The Global Economy
• International economy
affects firm prospects.
• Performance in countries
and regions can be highly
variable.
• Harder for businesses to
succeed in contracting
economies than in
expanding ones.
Political and exchange
rate risk!
Macroeconomic Variables and Terms
• Gross domestic product
• Unemployment rates
• Inflation
• Interest rates
• Budget deficit
• Sentiment
• The transition points across
business cycles are called peaks
and troughs
• Peak: transition from the end of
an expansion to the start of a
contraction.
• Trough: occurs at the bottom of a
recession just as the economy
enters a recovery.
Business Cycles
Business Cycles
Cyclical Industries
• Above-average sensitivity to the
state of the economy
• Examples:
• Consumer durables
• Capital goods
• High betas
Defensive Industries
• Little sensitivity to the business
cycle
• Examples:
• Food producers and processors
• Pharmaceutical firms,
• Public utilities
• Low betas
Business Cycles
Business Cycles
1. Sensitivity of sales
• Necessities vs. discretionary goods
• Items that are not sensitive to income levels (such as tobacco and movies) vs.
items that are, (such as machine tools, steel, autos)
2. Operating leverage
• Firms with low operating leverage (less fixed assets) are less sensitive to
business conditions
• Firms with high operating leverage (more fixed assets) are more sensitive to
the business cycle
3. Financial leverage
• Interest is a fixed cost that increases the sensitivity of profits to the business
cycle
Macroeconomic Indicators
Building a portfolio
Passive management:
• Buy the market portfolio.
Active management:
• Identify mispriced securities through a valuation process
• Compose a portfolio with respect to the risk-reward profile of the
mispriced securities and mix it in with the passive portfolio.
Review: Single Factor Model
• Return is composed of stock outperformance / underperformance
and captured market risk premium:
E 𝑅𝑖 = 𝛼𝑖 + 𝛽𝑖 𝐸(𝑅𝑀 )
• Variance is composed of systematic risk and firm-specific risk:
2
𝜎𝑖2 = 𝛽𝑖2 𝜎𝑀
+ 𝜎 2 𝑒𝑖
Diversify the firm-specific risk away!
Portfolio Construction w/ Single-Factor Model
• Expected return of the portfolio:
𝐸 𝑅𝑃 = 𝛼𝑃 + 𝛽𝑃 𝐸(𝑅𝑀 )
• Standard deviation of the portfolio:
𝜎𝑃 =
• Sharpe ratio:
2
𝛽𝑃2 𝜎𝑀
+ 𝜎 2 𝑒𝑃
𝐸 𝑅𝑃
𝛼𝑃 + 𝛽𝑃 𝐸(𝑅𝑀 )
S𝑃 =
=
2
𝜎𝑃
𝛽𝑃2 𝜎𝑀
+ 𝜎 2 𝑒𝑃
Back to Building of Portfolios
• We considered three main parameters per stock:
• Alpha of stocks
• Beta of stocks
• Individual surprises as the residual variances
• Assumption: residuals are uncorrelated.
• Goal: Improve the passive portfolio by adding an active part in which
we do security selection.
How to build your portfolio
• Compute the initial position of each
security.
• Apple (stock 1)
• 𝛼1 = 0.02, 𝜎 2 𝑒1 = 0.08
• If you have high alpha, you’d like more.
• Tesla (stock 2)
• If the stock has high firm-specific risk, you’d
• 𝛼2 = 0.04, 𝜎 2 𝑒2 = 0.48
like less.
Then:
0
2
𝑤𝑖 = 𝛼𝑖 /𝜎 (𝑒𝑖 )
• Scale the positions such that the sum of
your weights is one: 0
𝑤𝑖
𝑤𝑖 =
σ𝑖 𝑤𝑖0
• 𝑤10 = 0.02Τ0.08 = 0.250
• 𝑤20 = 0.04Τ0.48 = 0.083
Rescale: 𝑤10 + 𝑤20 = 1Τ3
𝑤10ൗ
𝑤1 =
0.333 = 0.750
•
• 𝑤2 = 0.250
How to build your portfolio
• Compute the abnormal return
𝛼𝐴 of your active portfolio:
𝛼𝐴 = ෍ 𝑤𝑖 𝛼𝑖
𝑖
• Compute residual variance of
your active portfolio coming
from the individual securities:
𝜎 2 𝑒𝐴 = ෍ 𝑤𝑖2 𝜎 2 (𝑒𝑖 )
𝑖
• Apple: 𝛼1 = 0.02, 𝑤1 = 0.75
• Tesla: 𝛼2 = 0.04, 𝑤2 = 0.25
Then:
𝛼𝐴
= 0.75 × 0.02 + 0.25 × 0.04
= 0.025
• 𝜎 2 (𝑒1 ) = 0.08, 𝑤12 = 0.5625
• 𝜎 2 𝑒2 = 0.48, 𝑤22 = 0.0625
Then:
𝜎 2 𝑒𝐴
= 0.5625 × 0.08 + 0.0625 × 0.48
= 0.075
How to build your portfolio
• Compute how much you want
to have in A given the risk and
return (like for the individual
securities before):
𝑤𝐴0 =
𝛼𝐴
𝜎 2 𝑒𝐴
൙E 𝑅
𝑀
2
𝜎𝑀
• 𝛼𝐴 = 0.025
• 𝜎 2 𝑒𝐴 = 0.075
=>
𝛼𝐴
𝜎 2 𝑒𝐴
= 1/3
Let’s assume the market risk premium for
the next year is 8%, and the std. deviation
of the market is 20%. Then:
• E 𝑅𝑀 = 0.08
2
• 𝜎𝑀
= 0.04
Therefore, 𝑤𝐴0 =
=>
E 𝑅𝑀
2
𝜎𝑀
1/3
= 1/6
2
=2
How to build your portfolio
• Find the beta of this active portfolio, which is the weighted sum of all
the individual securities’ beta:
𝛽𝐴 = ෍ 𝑤𝑖 𝛽𝑖
𝑖
• Depending on the securities and the weights we assigned, 𝛽 might be
quite different than 1. If our beta is very high, then the passive
portfolio becomes less and less beneficial for diversification.
0
𝑤
𝐴
∗
𝑤𝐴 =
1 + 1 − 𝛽 𝑤𝐴0
• Finally, calculate how much should go in A and how much in M.
Treynor-Black Model
• The optimization uses analysts’ forecasts of superior performance.
• Problems:
• The optimal portfolio calls for extreme long/short positions that may not be
feasible for a real-world portfolio manager if we find large positive or negative
forecasts for alpha.
• The portfolio is too risky and most of the risk is nonsystematic risk.
• Restricting extreme positions however reduces diversification..
Treynor-Black Model
Two slightly different forecasts lead to a
lot of differences in weights in individual
components and overall weights!
Weight of active portfolio: 22.98%
Weight of active portfolio: 16.14%
Treynor-Black Model
Treynor-Black Model with Constraints
Treynor-Black Model with Constraints
• We still have fairly large weights in individual positions because we
believed in their superior or inferior performance.
• Positions came based on our forecast of their alphas.
• Before committing, we should ask:
• How sure are we of our forecast, or
• How big is our precision of the forecast alpha?
• Study tracking error, meaning the past performance of our forecasts,
then adjust the position with an adjusted alpha.
Portfolio Performance Evaluation
Very early, we recognized that just comparing returns is not the most
appropriate way to measure performance – we must adjust for risk!
• The simplest way to adjust for risk is to compare the portfolio’s return
with the returns of a comparison universe
• The comparison universe is called the benchmark
• It is composed of a group of funds or portfolios with similar risk
characteristics
Adjusting Returns for Risk
Benchmark or universe comparison
over different time horizons!
• Compare to S&P 500 and the range.
• Lines indicate the median as well as
the 25% and 75% quantile.
• How well is The Markowill Group
doing?
Benchmarking
Characteristics of a good benchmark:
1. Well defined, i.e., verifiable and free of ambiguity.
2. Tradeable, i.e., an investor should be able to invest in it.
(Fama-French factors are not tradeable.)
3. Replicable, either through building a portfolio or buying an index
fund.
4. Adjusted for risk, i.e., incorporating 𝛽.
Benchmarking – Example
Build an equal-weight portfolio out of 10 tech stocks:
• AAPL, AMD, AMZN, CRM, FB, GOOG, MSFT, NFLX, NVDA, PANW.
Benchmark idea: QQQ.
1.
2.
3.
4.
Well defined
Tradeable
Replicable
Adjusted for risk
✅
✅
✅
❌
Benchmarking – Example
Build an equal-weight portfolio out of 10 tech stocks:
• AAPL, AMD, AMZN, CRM, FB, GOOG, MSFT, NFLX, NVDA, PANW.
Benchmark idea: QQQ.
Regression Results:
• 𝛽QQQ = 0.9715
===> The benchmark is 0.9715 x Market
• 𝛽𝑃
= 1.1410
===> The portfolio is
1.1410 x Market
Portfolio “overperformance“ is expected!
Proper Benchmarkings
• Run a regression of the portfolio as Y and the benchmark as X, like in
the single-factor model (not CAPM):
𝑟𝑃 − 𝑟𝑓 = 𝛼 + 𝛽 𝑟𝑄𝑄𝑄 − 𝑟𝑓 + 𝑒.
• We find that 𝛽 = 1.2556, i.e., the portfolio fluctuates more!
• The true benchmark for the portfolio is
𝑟𝑏𝑚𝑘 = −0.2556 𝑟𝑓 + 1.2556𝑟𝑄𝑄𝑄 ,
where we borrow to buy more QQQ.
Benchmarking – Example
Build an equal-weight portfolio out of 10 tech stocks:
• AAPL, AMD, AMZN, CRM, FB, GOOG, MSFT, NFLX, NVDA, PANW.
Benchmark idea: QQQ.
1.
2.
3.
4.
Well defined
Tradeable
Replicable
Adjusted for risk
✅
✅
✅
✅
Metrics for Risk-Adjusted Performance
We learned a few of these already, maybe under different names:
• Sharpe ratio
• Modigliani-Squared
• Treynor measure
• Jensen’s alpha
• Information ratio
Metrics for Risk-Adjusted Performance
Sharpe ratio:
𝑟𝑃 − 𝑟𝑓
SR =
𝜎𝑃
Where we plug in:
• Average return on the portfolio
• Average risk free rate
• Standard deviation of returns for portfolio
Metrics for Risk-Adjusted Performance
How do we interpret the Sharpe ratio?
• We can compare two investments or portfolio over the same time horizon and say
which one was better, but the numerical value is hard to interpret…
Idea: Use Modigliani-Squared instead.
• Remember: Combination of Portfolio and
risk-free Treasury bills forms CAL(P)
• We can increase or decrease position in T-bills
to tune risk.
• Tune such that P and market portfolio M have
the same risk. Then compare return!
Metrics for Risk-Adjusted Performance
Example:
Managed Portfolio P:
𝑟𝑃 = 35% 𝜎𝑃 = 42%
Market Portfolio:
𝑟𝑀 = 28% 𝜎𝑀 = 30%
T-bill return = 6%
Tune our synthetic portfolio:
• P*: 30/42 = 0.714 in P; and 0.286 in T-bills
• 𝑟𝑃∗ = 0.714 × 35% + 0.286 × 6% = 26.7%
• 𝑟𝑃∗ < 𝑟𝑀 meaning the managed portfolio underperformed; by 1.3%! Metrics for Risk-Adjusted Performance Treynor ratio: 𝑟𝑃 − 𝑟𝑓 Treynor = 𝛽𝑃 Where we plug in: • Average return on the portfolio • Average risk free rate • Weighted average beta for portfolio Metrics for Risk-Adjusted Performance Jensen’s Measure giving the alpha of the portfolio: 𝛼𝑃 = 𝑟𝑃 − 𝑟𝑓 + 𝛽𝑃 𝑟𝑀 − 𝑟𝑓 Where we plug in: • Average return on the portfolio • Average risk free rate • Weighted average beta for portfolio • Average return on the market index portfolio Metrics for Risk-Adjusted Performance Information Ratio: 𝛼𝑃 𝑆= 𝜎(𝑒𝑃 ) Where we plug in: • 𝛼 of the portfolio • Standard deviation of the error terms in the portfolio which is the non-systematic risk. In theory, we could diversify this away, but in our selection for 𝛼, it’s not always possible. Metrics for Risk-Adjusted Performance Which one to use? • It depends on investment assumptions • If P is not diversified, then use the Sharpe measure as it measures reward to risk in general. • If the P is diversified, nonsystematic risk is negligible and the appropriate metric is Treynor’s, measuring excess return to beta. • If we want to to mix P with a benchmark portfolio, we can evaluate the benefit by considering the information ratio. Metrics for Risk-Adjusted Performance Example: Which portfolio is better, P, Q, or the market? Standard Deviations: P: 9.5%, Q: 15.6%, Market: 8.8% Sharpe Ratios? Metrics for Risk-Adjusted Performance Example: Standard Deviations: P: 9.5%, Q: 15.6%, Market: 8.8% 11% SR 𝑃 = = 1.16 9.5% 19% SR 𝑄 = = 1.23 15.6% 10% SR 𝑀 = = 1.14 8.8% Metrics for Risk-Adjusted Performance For Treynor, we can plot the return as a function of beta which is what we determined for the portfolio as the weighted average! • Market portfolio has slope of excess return divided by 1. (Why?) Metrics for Risk-Adjusted Performance • If P or Q represents the entire investment, the one with the higher Sharpe ratio is better -- in this case Q. • If P and Q are competing for a role as one of a number of subportfolios, Q also dominates because its Treynor measure is higher Performance Measure over Time • We need a very long observation period to measure performance with any precision, even if the return distribution is stable with a constant mean and variance. • Think about statistical analysis and t-statistics and confidence intervals... • Example: • Jensen’s alpha of a fund is, over a period of 8 years: +4.5%, -0.4%, +0.4%, +9.2%, -1.3%, +0.9%, +0.8%, +1.7%. • Mean of alpha: 1.975%. Sample standard deviation of alpha: 3.163%. • 95% Confidence interval: [-0.217%, +4.167%]. • What if the mean and variance are not constant? We need to keep track of portfolio changes Style Analysis Question: How much of the performance stems from asset selection and how much comes from portfolio composition by groups of assets? Style analysis introduced by William Sharpe • Regress fund returns on indexes representing a range of asset classes • The regression coefficient on each index measures the fund’s implicit allocation to that “style” • R-square measures return variability due to style or asset allocation • The remainder is due either to security selection or to market timing Style Analysis Homework AD 717 Week 10 Unless stated otherwise, round your answers to three decimals, and do not round intermediate calculations. Building an active portfolio. In this problem, we will build an active portfolio, that is, a portfolio consisting of individually selected stocks to complement our passive investments. To do this, create an Excel worksheet. Use the following instructions with a market risk premium 𝑟" − 𝑟$ of 5%. Consider the following annualized information regarding a selection of six stocks (Apple Inc, Amazon.com Inc, Intuitive Surgical Inc, Target Corp, Walmart Inc, and Exxon Mobil Corp) and the S&P 500 that we have obtained from a regression analysis: • • • SD of Excess Return Beta SD of Systematic Component SD of Residual S&P 500 0.1701 1.00 0.1701 0.0000 $AAPL 0.2869 1.20 0.2041 0.2016 $AMZN 0.3554 1.60 0.2721 0.2286 $ISRG 0.3409 1.50 0.2551 0.2261 $TGT 0.2761 0.80 0.1361 0.2403 $WMT 0.2296 0.60 0.1020 0.2057 $XOM 0.2163 0.85 0.1446 0.1609 Find the covariance matrix according to the index model, where the covariance between two 1 1 assets is defined as 𝐶𝑜𝑣(𝑟) , 𝑟+ , = 𝛽) 𝛽+ 𝜎" . [Hint: You can find the 𝜎" from the above table if you compute the covariance of the index with itself because 𝛽2&4 566 = 1.] Create a forecast of 𝛼) for each company, that is, the return in percent you anticipate in excess over the return expected through its 𝛽) in the coming year. [Example: If the 𝛽 of the company were to be 1, you’d expect an excess return of 5% in the absence of 𝛼. However, if you anticipated that the company’s stock was going to realize an excess return of 4% or 6%, then its 𝛼 would be -1% or +1%, respectively.] This forecast can just be a guess for this problem! Construct the risky portfolio according to Table 27.1 in your book or according to “How to build your portfolio” in today’s lecture slides. Compute and report the following parameters for your portfolio: 1. 2. 3. 4. Weights of the securities in your active portfolio and its 𝛼. Weight of the active portfolio in the overall portfolio. Aggregate alpha and beta of the active portfolio and of the overall portfolio. Compare the Sharpe ratio of an investment in the market with the Sharpe ratio of the overall portfolio you have constructed! You need to report answers with your own assumptions. But you can check your work with: Alpha AAPL 0.5% AMZN 0.5% ISRG 1.0% TGT -0.5% WMT 1.0% XOM -0.8% Using these values for each stock, your active portfolio should have 𝛼4 = 3.263%, 𝛽4 = 1.584. The overall portfolio should come out to 𝛼A = 0.527%, 𝛽A = 1.094. The Sharpe ratio of this overall portfolio is 0.308, whereas the Sharpe ratio of the market portfolio is 0.294. Purchase answer to see full attachment

  
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