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### InvestmentsMBA 536

### Break Time

Dr. David P Echevarria

Cameron School of Business

University of North Carolina Wilmington

Unit 2: Risk and Return

- Unit 2 begins our journey into the fundamental analysis of risk and return. As we delve into the statistical nature of risk measurement, we must remind ourselves that the market is always and everywhere an expectations phenomenon. We don’t really know a lot about the future. We know quite a bit about the past and attempt to use it as a guide to discerning the future. A caution is warranted as we observe the elaborate mathematical and statistical models that purport to explain the market’s behavior. We note with interest the disclaimer in every prospectus; “…past performance is no guarantee of future performance, investigate before you invest…”

Chapter 5: Introduction to Risk and Return

I.STUDENT LEARNING OBJECTIVES

- Therole of supply and demand for funds
- The concept of market equilibrium
- How does the government affect supply and demand?
- Can we predict future interest rates?
- The risk premium concept

Chapter 5: Introduction to Risk and Return

II. DEMAND FOR [LOANABLE] FUNDS

- Households
- Consumption and saving a function of income
- Consumption above current income levels financed with borrowing.
- Business
- Finance asset expansion (20% using external capital)
- Government
- Demand for funds Inelastic with respect to rates.
- Foreign
- Additional sources of risk – exchange rate volatility

Chapter 5: Introduction to Risk and Return

III. SUPPLY OF LOANABLE FUNDS

- Households are net suppliers of funds.
- The supply of funds is a function of risk and return.
- The supply of funds is also subject to investor preferences.
- Governments may also supply funds (credit or specie).

Chapter 5: Introduction to Risk and Return

IV. EQUILIBRIUM INTEREST RATE

- Equilibrium ≡ point at which markets clear (no excess supply or demand).
- Question: Is an equilibrium point observable?
- Question: Is equilibrium an important concept?
- Changes in the Equilibrium Interest Rate
- Change in response to changes in supply of funds
- Change in response to changes in demand for funds
- Fisher Effect: accounting for effects of inflation

Chapter 5: Introduction to Risk and Return

V. KEY ISSUES REGARDING INTEREST RATES

- Does US Gov’t borrowing affect rates?
- What impact do foreign rates have on domestic rates?
- What other exogenous events affect interest rates?
- Do shortages in the commodities markets affect rates?
- The short answer to the above questions: How do these things affect investor perceptions of economic risk? Once we have settled the risk question (and its time frame dimension) we can begin to understand how rates are set and how these rates influence economic activity.

Chapter 5: Introduction to Risk and Return

VI. FRAMEWORK FOR FORECASTING INTEREST RATES

- Factors in forecasts
- Foreign vs. Domestic household demand
- Foreign vs. Domestic household supply
- Business demand (a function of opportunities)
- Government demand

Chapter 5: Introduction to Risk and Return

VII. RISK AND RISK PREMIUMS

- What is risk?
- Probability - the chance of something occurring
- Uncertainty - the probability that the actual return may differ from the expected return
- Measuring risk
- Standard deviation: statistical measure of dispersion around a mean.
- Range: the difference between the highest and lowest values.

Chapter 5: Introduction to Risk and Return

VII. RISK AND RISK PREMIUMS (cont’d)

- Relationship between risk and return
- The expectation of higher returns requires taking greater risk
- Risk tolerance a function of the incentives to accept risk
- Risk Premium
- The difference between the return on a risky investment and the risk free rate
- Example: The 40-year average return on the SP500 is approximately 11%. The 30-day T-Bill has average about 5% for the same period. That suggests a risk premium of about 6% for the SP500. (T-Bill assumed to be risk-free – well almost!)

Chapter 5: Introduction to Risk and Return

VII. RISK AND RISK PREMIUMS (cont’d)

- Required Rate of Return
- Required (Expected) Rates of Return (RROR) are the building blocks of financial/economic analysis. The term “required” suggests that the investor has some control over the outcome of investment activity. Nothing could be further from the truth. We have expectations, especially with equity investments, and expectations like hope end in fruition.
- Nominal Rate = Real rate of return + Expected rate of inflation + Default premium
- Risk is modeled on the expectation that outcomes are normally distributed about some expected mean.
- The Normal Distribution of Events Fallacy (Taleb’s Ludic Fallacy)

Chapter 6 Risk Aversion and Capital Allocation

I. RISK AND AVERSION

- Risk: chances that the actual will not be the expected.
- Speculation: when greed beats out rational judgment
- Gambling: the attempt to beat the odds (cousin to speculation)
- Capital Allocation
- Assumes we have linked risk tolerance, objective time horizon, and opportunity sets
- The mix of investments, modified over time as necessary, to achieve a stated [wealth] objective.
- Reflects the decisions of a rational, end of period, wealth maximizing [economic] individual.

Chapter 6 Risk Aversion and Capital Allocation

II. UTILITY THEORY

- What is the utility of an additional unit of wealth? Some will labor all day to increase their wealth endowment by 1 unit of wealth. Others may not be willing to expend the time and effort necessary to do so. The latter have other preferences for the use of their time and energy. In effect, utility theory seeks to establish our priorities or preferences.
- Question: which would you prefer?
- Three new shirts and two pairs of new slacks or
- Two new shirts and three pairs of new slacks

Chapter 6 Risk Aversion and Capital Allocation

II. UTILITY THEORY (cont’d)

- Question: how much effort would you expend to make an additional dollar of income?
- Little or None at all
- Whatever it takes
- Question: how do you feel about risk (probability of loss)?
- I would jump off a bridge if I lost all my money
- Easy come - easy go – tomorrow is another day
- Getting from here to there while attempting to maximize value and minimize risk

Please be back in 15 minutes.

Chapter 7: Diversification and Risk

- Student Learning Objectives
- Why Diversification is important
- What are the two principal sources of investment risk
- Standard deviation as a measure of risk for individual securities and portfolios
- Security correlation and portfolio risk
- Modern Portfolio Theory (MPT): Theory and Practice

Chapter 7: Diversification and Risk

II. DIVERSIFICATION

- Portfolio diversification
- Diversification can reduce the risk
- Benefits of diversification increase as average correlation decreases
- Two Principal Source of [Investment] Risk
- Market (systematic) risk: Effects of business cycles and economic factors on earnings
- Firm-specific (idiosyncratic) risk is tied to the company’s contracts, products, etc.

Chapter 7: Diversification and Risk

- Portfolio Risk: Standard deviation of expected returns
- [Statistical] diversification
- Increasing the number of stocks reduces the portfolio risk from any individual stock
- Diversification across time
- Annualized standard deviations decline as the investment horizon increases
- Uncertainty also increases and total return may not improved
- Naive Diversification
- Occurs when investors select stocks at random
- When N becomes large enough; only systematic risk

Chapter 7: Diversification and Risk

- Correlation and Portfolio Risk: Essence of MPT
- Each pair of assets in a portfolio has some degree of correlation.
- If, on average, asset pairs have high positive correlation, then Pf risk is greatest.
- If, on average, asset pairs have low positive or negative correlation, then Pf risk is less.
- MPT suggests holding large well diversified portfolios as the best strategy for minimizing the effects of idiosyncratic (variation) risk as well as correlation risk.

Chapter 7: Diversification and Risk

III. Modern Portfolio Theory (H. Markowitz)

- Prior to the development of Modern Portfolio Theory (MPT), investment portfolios were largely analyzed on the basis of returns.
- MPT suggests that portfolio performance should be defined in terms of the variance of returns and that variance (risk) is positively correlated with returns.
- The greater the variance, the greater the risk
- The riskiness of any portfolio was a function of the variance of individual securities and the average covariance of each pair of securities in the portfolio.
- The locus of efficient portfolios forms the efficient frontier.
- The shape of the efficient frontier is a function of the [average] correlation of the assets comprising the portfolio.

Chapter 7: Diversification and Risk

III. Modern Portfolio Theory (cont’d)

- Computing Portfolio Risk
- The Two-Asset Portfolio: Capturing the essential elements of MPT

Expected Return: E(rp) = W1 E(r1) + W2 E(r2)

Portfolio Variance: s2p = W21s21 + W22s22 + 2 W1W2 Cov (r1,r2)

Covariance (r1,r2): Cov (r1,r2) = S [{r1 – E(r1)}{r2 – E(r2)}] / n

- Portfolio variance (risk) is minimized when the average covariance is negative.
- The weights (Wi) are equal to the percentage of the portfolio’s value which is invested in each security
- The variance of a (n > 2) portfolio is more complex; it is a weighted average of the variances of each security and the correlation between each pair of securities
- For a Pf with 20 securities, there are 20 variances plus (20*19) covariances = 400 calculations.

Chapter 7: Diversification and Risk

- The impact of Co-movement (Correlation)
- When the holding period returns of two securities move in the same direction, by the same amount at the same time, the pair is perfectly positively correlated. r = 1
- When the holding period returns of two securities are totally unrelated to each other, the pair is uncorrelated. r = 0
- When the holding period returns of two securities in the opposite direction, by the same amount at the same time, the pair is perfectly negative correlated. r = -1
- Defining the Efficient Frontier

A line graphing the most efficient possible combinations of stocks for maximizing portfolio returns while minimizing portfolio risk - the best risk/return tradeoff

Chapter 7: Diversification and Risk

- PRACTICAL ASPECTS OF MEASURING RISK AND RETURN
- Expected Future prices as function of states of nature
- Variance computed after “A”
- Variance → standard deviation as measure of risk
- Simple method: range of returns (negative to positive)
- Use [recent] historic data to compute mean and SD – assume near future to look like recent past.
- Computing coefficient of variation (CV) as a means for rank-ordering investment possibilities in terms of riskiness. Recall that the CV is a scale free measure.

Chapter 7: Diversification and Risk

- Portfolio risk and return
- In general, the purchase of a single stock is a speculation, rather than an investment
- The owner of single security hopes to profit from an increase in the price of the security during the near term
- Profits and losses derived from near term changes in the price of a single asset are speculative in nature, and do not constitute investment returns
- Investing involves buying and holding a portfolio of securities, expecting to profit in the long term from the secular price trend of the market
- Portfolio diversification can reduce the risk an investor must bear without reducing the return an investor can expect to earn

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