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Introduction to Economics Elements of Personal Finance Llad Phillips 1 4. Thursday, Oct 8, Lecture Four: "Markowitz Efficiency Portfolio Analysis" Wall Street Journal Video, Guide to Money and Markets ( on reserve in Kerr Hall) Markowitz Efficient Portfolio Analysis Reading Assignment: Guide to Understanding Personal Finance, Ch. 5, "Investing" O’Sullivan and Sheffrin: Ch. 4, “Supply, Demand and Market Equilibrium” emphasis: the law of demand and market supply Problems O & S Text p. 78: 1, 2, 3, 4, 5, 6, 7 Llad Phillips 2 Outline: Lecture Four Video Guide to Money and Markets Interest rate, % per year, APR Determinants of Personal Income (cont.) Markowitz Efficient Portfolio Analysis Llad Phillips 3 Interest Rate Per Year On A Loan Example: One Payment loan amount: $1000 annual interest rate: 10% one payment at the end of the year pay back principal: $1,000 pay the interest on $1000 for a year: $100 principal*interest rate = interest $1000*0.1 = $100 total Llad Phillips payment due: $1100 4 Interest Rate Per Year On A Loan Example: Twelve Monthly Payments loan amount: $1000 annual interest rate: 10% Twelve Monthly Payments pay back principal of $1000 pay interest on the amount owed declining amount owed since you pay back some principal each month, until balance of principal owed is zero after twelve payments use Excel’s PMT function to calculate Llad Phillips 5 one payment of principal plus interest at the end of the year Principal $1000 Declining Balance, 12 monthly payments one Time year Llad Phillips 6 Twelve Monthly Payments loan interest rate, per year monthly payments 1000 10% 12 ($87.92) total payments -1054.99 interest Llad Phillips 54.99 7 Determinants of Personal Income Life Cycle Model Learning and Earning Your Market Wage Depends on your human capital Allocating your time between Learning and Earning 24 hour endowment your tastes for learning versus earning Llad Phillips 8 Earnings $480 Opportunities for trading leisure for earnings (income) at a rate, $20 per hour, the market wage, determined by your stock of human capital(step one of the paradigm: describing the alternatives for choice) $0 0 hours Llad Phillips 24 hours Leisure (learning) 9 Choosing Between Learning and Earning How much time for learning? How much time for earning? This choice, like all choices depends on your tastes Do you want to earn and consume now? Do you want to learn, earn more in the future, and consume more in the future? Llad Phillips 10 Economists Assume You Can make Comparisons example: more leisure and less income versus less leisure and more income recall Llad Phillips Lecture One: an Altima Vs. a Taurus 11 Economists Assume You Can Make Tradeoffs How much income will you demand to give up your leisure? Llad Phillips 12 Depicting your tastes graphically: iso-preference or indifference curves Earnings $480 Iso-Preference Curves: You value all points on a curve equally(step two of the paradigm: valuing the alternatives for choice) $0 0 hours 24 hours Leisure (learning) Depicting your tastes graphically Earnings low value $480 high Iso-Preference Curves: You value all points on a curve equally high value $0 0 hours Leisure 24 hours (learning) The choice between leisure and earning now:picking the best alternative Earnings high $480 alternatives $0 0 hours Iso-Preference Curves: You value all points on a curve equally high value low value 24 hours Leisure (learning) Individual’s Supply of Labor Earnings low value $480 $180 for 9 hrs of work high Optimum high value Leisure (learning) $0 0 hours 15 hours of leisure 24 hours Personal Investing How do you choose between stocks or bonds as a personal investment? How do you choose between mutual funds? Are stocks and bonds too risky? Should you keep your money in cash or gold? Llad Phillips 17 Example: UC Funds Suppose you invest up to $9,500 per year in a tax sheltered 403(b) plan you have to save $9,500, but you would have to pay income taxes if you took it as income UC investment alternatives guaranteed insurance contract(GIC) savings fund money market fund bond fund stock index fund multi-asset fund Llad Phillips 18 Investment Concepts monthly return for June 1998 on an asset price(June) - price(May) + dividends price(June) - price(May): capital gain(loss) dividends(interest): income from stocks(bonds) monthly rate of return for June 1998 [price(June) - price(May) + dividends]/price(May) in %, multiply by 100 • annual rate: multiply by 12 Llad Phillips 19 Example: UC Funds/Mutual Funds Sources of information on UC funds monthly, quarterly, annual, etc. rates of return internet: http://www.ucop.edu/bencom/rs/perform.html Notice, a publication of the UC Academic Senate Source of Information on Mutual Funds quarterly The Wall Street Journal, Mutual Funds Quarterly Review, e.g. extra section in July 3, 1997 Journal Llad Phillips 20 UC Funds: Monthly Rate of Return 8 6 2 97.05 97.03 97.01 96.11 96.09 96.07 96.05 96.03 96.01 -2 95.11 0 95.09 Rate 4 Equity Insurance -4 -6 Year:Month Llad Phillips 23 UC Funds: Equity Vs. Insurance Insurance steady at a rate of return of about 0.6 per month or 7.2% per year does not vary much never negative Llad Phillips Equity rate of return varies a lot from month to month range of rates of return from about plus 8% in Nov. ‘96 to minus 5% in July ‘96 can turn negative: 7 months out of 22 24 UC Funds Monthly Rate of Return 0.7 0.6 0.4 0.3 Insurance Money Market Savings 0.2 0.1 97.05 97.03 97.01 96.11 96.09 96.07 96.05 96.03 96.01 95.11 0 95.09 Rate 0.5 Year:Month Llad Phillips 25 UC Funds: Monthly Rates of Return 8 Bond Equity Multi-Asset 6 2 97.05 97.03 97.01 96.11 96.09 96.07 96.05 96.03 96.01 -2 95.11 0 95.09 Rate 4 -4 -6 Year:Month Llad Phillips 26 Two Kinds of Assets low rate of returnlow variability want high rate of return return on average want low variability predictable high return-high variability want high rate of return on average want low variability average return Dilemma: which kind of asset to hold? Llad Phillips 27 Investment Principles or Maxims Don’t hold put all of your eggs in one basket a diversified portfolio cash bonds stocks real estate advantage of a mutual fund instead of holding one stock, e.g. Coca-Cola, you hold a bundle of stocks Choose the asset with the highest reward for a given level of risk Llad Phillips 28 Measures of Average Rate of Return and Variability: Mean & Std. Dev. Date Bond 95.09 95.1 95.11 95.12 96.01 96.02 96.03 96.04 96.05 96.06 96.07 96.08 96.09 96.1 96.11 96.12 97.01 97.02 97.03 97.04 97.05 97.06 mean standard deviation Equity 2.66 2.4 3.9 2.83 -0.51 -5.42 -0.63 -0.75 0.78 1.68 0.34 0.35 4.21 7 5.56 -4.16 0.04 1.35 -3.59 2.23 2.59 2.75 1.16 3.00 Insurance 4 -0.26 4.07 -0.13 3.32 2.35 -0.24 1.6 2.56 -0.12 -5.01 2.33 4.59 0.39 7.69 -1.25 4.59 0.42 -2.33 4.09 6.16 3.5 0.64 0.66 0.64 0.66 0.64 0.6 0.64 0.61 0.63 0.61 0.63 0.63 0.61 0.63 0.61 0.62 0.62 0.56 0.64 0.6 0.62 0.6 1.92 2.95 0.62 0.02 Money Market Multi-Asset Savings 0.49 2.09 0.49 0.64 0.47 2.39 0.48 0.78 0.47 1.23 0.43 -0.12 0.45 0.02 0.43 0.62 0.44 1.27 0.44 0.5 0.46 -1.43 0.46 1.08 0.45 2.6 0.46 1.77 0.45 3.97 0.47 -1.1 0.46 1.82 0.41 0.62 0.45 -1.31 0.45 2.08 0.47 2.91 0.46 2.02 0.46 0.02 1.11 1.38 0.52 0.53 0.51 0.52 0.52 0.49 0.52 0.5 0.51 0.5 0.51 0.51 0.49 0.52 0.49 0.51 0.52 0.46 0.54 0.5 0.51 0.5 0.51 0.02 Mean Returns & Standard Deviations UC Funds: Mean Return Vs. Risk (Standard Deviation) 2.00 Equity 1.80 1.60 Mean Return 1.40 1.20 Multi-Asset Bond 1.00 0.80 0.60 Insurance Savings 0.40 Money Market 0.20 0.00 0.00 Llad Phillips 0.50 1.00 1.50 2.00 Standard Deviation 2.50 3.00 3.50 32 Efficient Investment Portfolio UC Funds: Mean Return Vs. Risk (Standard Deviation) 2.00 Equity 1.80 1.60 Mean Return 1.40 1.20 Multi-Asset Bond 1.00 0.80 0.60 Insurance Savings 0.40 Money Market 0.20 0.00 0.00 0.50 Llad Phillips 1.00 1.50 2.00 Standard Deviation 2.50 3.00 3.50 33 Your portfolio should be on the efficient frontier But where on the frontier? depends on your taste for reward and risk reward, i.e. the mean rate of return is a good risk is a bad Llad Phillips 34 Economic Paradigm: Valuation of Mean Return and Risk Assumption: Mean Return is Good, Risk is Bad: U =U(M,R) better Mean Return, M worse B C A Iso - Preference Curves Prefer B to A; Prefer B to C Llad Phillips Risk, R 35 Efficient Investment Portfolio UC Funds: Mean Return Vs. Risk (Standard Deviation) 2.00 Investor A: very risk averse 1.80 Equity 1.60 Mean Return 1.40 1.20 Multi-Asset Bond 1.00 0.80 0.60 Insurance Savings 0.40 Money Market 0.20 0.00 0.00 0.50 Llad Phillips 1.00 1.50 2.00 Standard Deviation 2.50 3.00 3.50 36 Efficient Investment Portfolio UC Funds: Mean Return Vs. Risk (Standard Deviation) 2.00 Investor B: not very risk averse Equity 1.80 1.60 Mean Return 1.40 1.20 Multi-Asset Bond 1.00 0.80 0.60 Insurance Savings 0.40 Money Market 0.20 0.00 0.00 0.50 Llad Phillips 1.00 1.50 2.00 Standard Deviation 2.50 3.00 3.50 37 Efficient UC Investment Portfolio f*insurance where contract + (1-f)*equity fund f can range from zero to one example: 50:50, i.e one half of your nest egg is invested in the Insurance Contract and the other half is invested in the Equity Fund. • mean return: 1/2 *0.62 + 1/2*1.92 = 1.27 % per month • expected risk(standard deviation: 1/2*0.02 + 1/2*3.02 =1.52 Llad Phillips 38 –exercise: show that this mean portfolio return –and expected risk lie on the efficient frontier – connecting the insurance contract and the –equity fund Llad Phillips 39 Summary-Vocabulary-Concepts Markowitz Portfolio Analysis stock index fund bond fund money market fund guaranteed insurance contract monthly rate of return Llad Phillips capital gains dividends mean rate of return on an asset risk of holding an asset a risk averse person investment portfolio 40 Return -5 -10 Llad Phillips 98.07 98.05 98.03 98.01 97.11 97.09 97.07 97.05 97.03 97.01 96.11 96.09 96.07 96.05 96.03 96.01 95.11 95.09 UC Funds: Monthly Rates of Return 10 5 0 Bond Equity -15 Date 41