Risk Spread Empirics

4. RISK-RETURN NEXUS:
EMPIRICAL EVIDENCE
FROM THE CAPM

5. Title and Content Layout with List
 Concept of Risk
 Concept of Return
 Financial Decision
 Risk Portfolio Diversification and Indifference Curve

6. What is risk?
Risk is the potential for divergence between the actual
outcome and what is expected.
In finance, risk is usually related to whether expected cash
flows will materialize, whether security prices will fluctuate
unexpectedly, or whether returns will be as expected.
Risk is a measure of the uncertainty surrounding the return
that an investment will earn or, more formally, the variability
of returns associated with a given asset.

7. Types of Risk
Systematic Risk Unsystematic Risk
•Risk factors that affect a
large number of assets
•Also known as non-
diversifiable risk or market
risk
•Includes such things as
changes in GDP, inflation,
interest rates, etc.
•Risk factors that affect a
limited number of assets
•Also known as unique risk
and asset-specific risk
•Includes such things as labor
strikes, part shortages, etc.

8. Total Risk
Total risk = systematic risk + unsystematic risk
The standard deviation of returns is a measure of
total risk
For well-diversified portfolios, unsystematic risk is
very small
Consequently, the total risk for a diversified portfolio
is essentially equivalent to the systematic risk

9. Total Risk = Systematic Risk + Unsystematic Risk

10. Systematic Risk Principle
There is a reward for bearing risk
There is not a reward for bearing risk unnecessarily
The expected return on a risky asset depends only on
that asset’s systematic risk since unsystematic risk
can be diversified away

11. Income received on an investment plus any
change in market price, usually expressed as a
percent of the beginning (average) market price
of the investment.
𝑅𝑡 = 𝐷𝑡+ 𝑃𝑡−𝑃𝑡−1
𝑃𝑡−1
What is Return?

12. Returns
Total Return = expected return + unexpected return
Unexpected return = systematic portion +
unsystematic portion
Therefore, total return can be expressed as follows:
Total Return = expected return + systematic portion +
unsystematic portion

13. The risk premium
The risk premium is the return on a risky security
minus the return on a risk-free security (often T-bills
are used as the risk-free security)
Another name for a security’s risk premium is the excess
return of the risky security.
The market risk premium is the return on the market
(as a whole) minus the risk-free rate of return.
We may talk about this much later in this study.

14. Keynote
Thus, effective risk pooling strategy that will guarantee
optimal returns associated with uncorrelated risk
portfolios. That is, a diversified risk portfolio
commands higher risk-returns tradeoff mix. This may
also warrant the need for risk sharing (the spreading of
risk between insurers according to percentage
retention capacity). On the whole, risk pooling and
sharing in insurance allows individuals underwriters to
deal many risks at affordable premiums.

16. Financial Decision and Risk Portfolio Diversification
Financial Decisions is a comprehensive financial planning and
wealth management firm that helps high-net-worth individuals
and businesses achieve their financial objectives.
Types of Financial Decisions
1. Investment decision (Capital Budgeting Decision)
2. Financing decision (Sources of Funding Decision)
3. Dividend decision
4. Liquidity Decision

17. Financial Decision
Cash Flow
Return on
Investment
Risk Involved
Investment
Criteria
Investment
Decision
Sources of
Funding (Owner
or Borrowed
Funds)
Cost of Capital
(Interest and
Exchange rates)
Financial Risk
(Inflation &
Business
Volatilities)
Financing
Decision
Earnings
Stability of
Earnings
Cash Flow
Position
Dividend
Decision
Solvency Margin
Reserves
Risk on Current
Assets
Investment
Profitability
Margin
Liquidity
Decision

18. Avenues for Diversification
Diversify
with asset
classes
Diversify
with index
funds
Diversify
among
countries
Evaluate
assets
Buy
insurance

19. Risk Portfolio Diversification and Indifference Curve
In economics, the analysis of consumer behavior
is performed using the indifference curve
approach. The indifference curve shows
consumption bundles that give the consumer the
same level of satisfaction. That is, the risk
appetite of an insurer on risk portfolios that
guarantees the highest risk premium in insurance.

20. Standard Behaviors towards Risk
RISK APPETITE EXPECTATIONS
INDIVIDUAL INSURANCE
DECISION
BUSINESS INVESTMENT
DECISION
A PRIORI BETA
RESULTS
Risk-Averse Favorable Outcomes May buy
Invest more and
underwrite major risk
exposures
β > 1.0 =
Aggressive
Risk-Neutral Indifferent Undecided
Indeterminate speculative
risk underwriting and
investment
β =1.0 Neutral
Risk-Lover All Outcomes Won’t buy
Invest little and
underwrite minor risk
exposures
β < 1.0 =
Defensive

21. Utility Theory
2
2
1
)( ArEU 
Utility of an investment
Expected return Variance or risk
Measure of risk tolerance
or risk aversion

22. Risk Preferences

23. Risk Reduction

25. CAPM is a model that describes the relationship between risk
and expected (required) return; in this model, a security’s
expected (required) return is the risk-free rate plus a premium
based on the systematic risk of the security.
Capital Asset Pricing Model (CAPM)
Under various assumptions about investors’ behavior, the
CAPM asserts that the market portfolio is mean variance
efficient, that is, it gives maximum expected return for a
given variance (level of risk).

26. The Capital Asset Pricing Model (CAPM)
Capital Asset Pricing Model or the CAPM provides a
relatively simple measure of risk.
CAPM assumes that investors choose to hold the
optimally diversified portfolio that includes all risky
investments. This optimally diversified portfolio that
includes all of the economy’s assets is referred to as the
market portfolio.
According to the CAPM, the relevant risk of an investment
relates to how the investment contributes to the risk of
this market portfolio. 26

27. The Capital Asset Pricing Model (CAPM)
The capital asset pricing model defines the
relationship between risk and return
If we know an asset’s systematic risk, we can
use the CAPM to determine its expected return
This is true whether we are talking about
financial assets or physical assets

28. Security Market Line
𝑅𝑗 = 𝑅𝑓 + 𝛽𝑗 𝑅 𝑀 − 𝑅𝑓
Investors
required
rate of
return for
stock j
Risk-free
investment
rate of
return
Beta,
measures
systematic
risk of stock j
Expected
return for
market
portfolio
Market Risk
premium

29. CAPM = SML

30. Security Market Line cont.

32. An index of systematic risk.
It measures the sensitivity of a stock’s
returns to changes in returns on the
market portfolio.
The beta for a portfolio is simply a
weighted average of the individual stock
betas in the portfolio.
What is Beta?

33. RISK – RETURN EMPIRICAL TOOLS
 Probability Distribution
 A listing of the various outcomes and the probability of
each outcome occurring
 Expected return
 A weighted average of the different outcomes multiplied
by their respective probability


n
i
ii RpRE
1
)(

34. Variance and Standard Deviation
Variance and standard deviation measure the
volatility of returns
Weighted average of squared deviations


n
i
ii RERp
1
22
))((σ

35. Portfolio Expected Returns
 The expected return of a portfolio is the weighted average of the
expected returns for each asset in the portfolio
 You can also find the expected return by finding the portfolio return
in each possible state and computing the expected value as we did
with individual securities


m
j
jjP REwRE
1
)()(

36. ECONOMETRIC ANALYSIS (CAPM)
To analyze the market risk premium model, we restate the CAPM as:
𝐋𝐢 = 𝛄𝐢 + 𝛃 𝐋 𝐦 − 𝛄𝐢 + 𝛍𝐢
The CAPM shall be analyzed using regression analysis.
The data used were derived from www.finance.yahoo.com, for the
period 2010-2017, on monthly basis.
Data information
• S&P 500 Stock Index, to proxy market return/portfolio
• Vanguard Government Short Term Bond, to proxy risk-free return
• JP Morgan Emerging Market Bond for LDCs, to proxy risk-free return
• Trust 20 year Treasury Bond, to proxy risk-free return

37. Analysis and Interpretation
Variable Beta-value Standard Error t Stat P-value
Alpha (0.01) 0.02 (0.28) 0.78
VGST BOND (41.28) 2.63 (15.69) 0.00
JP MORGAN EMB 6.09 0.71 8.57 0.00
TRUST 20YR T-BOND 36.12 2.14 16.85 0.00
The P-value results indicate that the portfolio assets analyzed are uncorrelated
and statistically significant at 0.95 levels.
Dependent Variable: S&P500 STOCK INDEX PORTFOLIO

38. Multiple R 1.00
R Square 1.00
Adjusted R Square 1.00
Standard Error 0.17
Observations 88.00
Regression Statistics

39. (500.00)
-
500.00
1,000.00
1,500.00
2,000.00
(20.00) - 20.00 40.00 60.00 80.00
S&P500STOCKINDEX
VGST BOND
VGST BOND Line Fit Plot
S&P500 STOCK INDEX
Predicted S&P500 STOCK
INDEX
2 per. Mov. Avg.
(Predicted S&P500
STOCK INDEX)

40. (500.00)
-
500.00
1,000.00
1,500.00
2,000.00
(50.00) - 50.00 100.00
S&P500STOCKINDEX
JP MORGAN EMB
JP MORGAN EMB Line Fit Plot
S&P500 STOCK INDEX
Predicted S&P500
STOCK INDEX
Linear (S&P500 STOCK
INDEX)
Linear (Predicted
S&P500 STOCK INDEX)

41. (500.00)
-
500.00
1,000.00
1,500.00
2,000.00
(50.00) - 50.00 100.00 150.00
S&P500STOCKINDEX
TRUST 20YR T-BOND
TRUST 20YR T-BOND Line Fit Plot
S&P500 STOCK INDEX
Predicted S&P500
STOCK INDEX
Linear (S&P500 STOCK
INDEX)
Linear (Predicted
S&P500 STOCK INDEX)

42. BRAVO!