Wharton Online Course: Module 1 Flashcards

Wharton Online Course: Module 1 Flashcards

MPT: Asset AllocationLong term view of what financial market and asset classes

can offer investors by way of reward, risk, and diversification Central TendencyExpected value or expected outcome (in units of time)The mean oraverage(mu)Used as what we should expect as the payoff Important Interpretations for Distributions How likely a given value is (for a discrete distribution)How likely a given range of values is (for a continuous

distribution)Example: In the standard normal (a bell curve

or Gaussian distribution), we know...- That approximately 95% of the observations fall between +/- 2 standard deviations from the mean (1.96 exactly)- The specific values of returns that give us that range Embeds the notion of optimal diversification Sharpe Ratio Example Generally, as volatility declines...Average annual returns declinesThe same as "high risk, high reward and low risk, low reward" Risk Free InvestmentAn investment where the return is the return you get for taking NO risk The higher the volatility...The greater the distinction between what you might expect in the average year and what you get when you string a series of years together and incorporate the potential downside than what you see in the upside (a volatility drag on returns) AKA the Tangency PortfolioThe portfolio combination where the Capital Market Line (the highest sloping Capital Allocation Possibility Lines) is tangent to the Frontier of Risky AssetsWhere the Capital Market Line slope equals the slope of the Frontier of Risky AssetsThe portfolio that does the best for you in terms of risk and reward Capital Market Line (CML) A variable that ranges from -100% to +100% representing the proportion of observations that an assets payoff moves in the same direction with respect to its central tendency (expected value) as does another Correlation Example

MPT: Tactical PlanningHappenings in the market place, Geo-Political events,

Change in expectations, Short term views from investors, advisors and portfolio managers History of Rates of Returns of Asset Classes Motivation for Thinking About Risk and Reward Random VariablesWe can use random variables to characterize quantities that are uncertain (like asset payoffs or returns)A variable that takes on particular values with a certain probability; this value represents an event or the state of the worldEx.

A "fair" coin that is flipped can be either "heads" or "tails", each with 50% probabilityWe can represent this numerically (ex. heads = 0, tails = 1) Standard Normal DistributionAKA Bell curve or Gaussian distributionA function of its central tendency and dispersion, with perfect symmetry and a known kurtosisKurtosis = 3

The minimum variance portfolioThe portfolio that of all

investment combinations minimizes volatilityNote:You'd

never invest below it because you can always have a higher reward with less risk The Efficient Frontier The "better" the correlation, the "better" the frontier -- more correlation means a frontier that extends further to the

northwest portion of the chartThink aboutdiversification: as

you add more assets to a portfolio in general, its variance decreases (even if assets individually have high risk)MPT gives a specific way of putting assets into portfolios that

theoretically minimizes risk/maximizes rewardNote:If we

have investments with the same expected return but with less than perfect positive correlation, total portfolio variability will decrease Correlation Two Fund SeparationThe aspect of MPT that says to invest in both risky assets and treasury bills in SOME proportionWe can split the investment decision into putting the risky portfolio together and one of combining a risky investment with financing (treasury bills) to delever or leverThe investment opportunity set is MUCH expanded as a result of this possibilityThe model suggests investors will want to hold aTangency Portfolio Modern Portfolio Theory FrameworkRisk-reward relationFramesmostrelevant issues -- Even if, at the end of the day, you don't think MPT is usefulIntimately connected to asset allocation and investment style analysis -- Techniques used by professional investorsInvestor Centric ModelProvides a structure for portfolio decisions Asset DistributionsDifferent assets have different shapes, and we associate risk and reward with themDistributions are usually similar to a standard normal distribution, but have some skewness and usually a higher level of kurtosis Random Variables ExampleIOMEGA is going to preview a new high capacity disk driveThe state of the world for IOM on that day can be modeled as a random variable (good, bad, neutral)Since IOMEGA's announcement would arguably result in particular states of the world with different likelihoods, we

can think of the probabilities as: Good = 1, p1 = 25%;

Neutral = 2, p2 = 50%; Bad = 3, p3 = 25%Note:All the

probabilities add up to 100%We could call good (X=1), neutral (X=2), bad (X=-1) if we wantedThe histogram is pictured Monitoring MPTAsset allocation, dynamics and implementationAdvantages and disadvantages of a historic track recordPortfolio rebalancing

Starting at an equity, as we allocate more of our wealth towards treasury bills, we will move to the left along the capital allocation possibility line towards to position "rf" with

declining risk and often declining returnNote:This allows us

to lower our volatility beyond the MVP and still maintain the same level of expected return Optimal Risky-Only Portfolio Every risky security can be combined with the riskless assetThese (infinite) combinations are made on thelineconnecting the riskless rate and a given risky securityThe most fundamental measure of the quality of these combinations is how much return for a given level of risk they provideTheslopeof thislineis known as the Sharpe

Ratio: See image

Why does the Sharpe ratio matter?

MPT: ImplementationExpression of investment allocations that arrive from

strategic and tactical planning (how to buy and sell)Active vs. passive Compounded vs. Average ReturnCompounded are usually lower (difference is approx. one half the variance)Compounded incorporates asymmetries -- the more volatile an investment, the lower the compounded annual rate of return The slope of the Capital Allocation Line investmentThe ratio of reward to risk for any given investmentExcess returns earned for taking risk divided by the volatility or risk for which you took any particular investment withThe rate at which we earn a return per unit of risk MPT Summary An infinity of potential outcomesThe Risk/Reward Relation: The Mean-Variance Frontier Riskless AssetA low-risk assetEx. Treasury billsAllows us to earn the risk-free investment return OR short-sell as a proxy to

finance positions and use leverageMPT:Invest in both risky

assets and treasury bills in SOME proportion Modern Portfolio Theory Just Says...If you expect reward, you should expect risk of some

varietyFor risky assets:Maximize return for a given level of

riskORMinimize risk for a given returnHow?Optimize -- Various quantitative methods & even some qualitative methodsThe result is known as the"mean-variance frontier"or"minimum variance frontier"or some variant What happens when you start stringing annual observations together for assets that have distributions with the same expectation but different levels of dispersionThe extremes are much larger for additional volatilityMean and median are greater for lower volatility Frontier Portfolio Expected REturn as a Function of Standard Deviation Perfect positive correlation has no beneficial trade-offOn the other hand, you can increase expected return for the same level of volatility or achieve the same return for a lower level of volatility by decreasing correlations between