Please see "image for quiz" file for references for the "Quiz 9" questions

1. (DO NOT NEED IMAGE FOR THIS ONE BUT YOU WILL NEED Z TABLE). A portfolio has an ECR of $17,000 and a Sigma cash return of $8,700, what is the probability that the portfolio will generate a cash return of less than $2,500 next year? A) 50% B) 0.00% C) 4.75% D) 95.25% 2. (DO NOT NEED IMAGE FOR THIS ONE, BUT YOU WILL NEED YOUR Z TABLE). A portfolio has a ECR of $10,000 and a Sigma Cash Return of $5,500. What is the probability that next years cash return will be less than $0? A) 55% B) 3.44% C) 0.00% D) 96.56% 3. The set of risk efficient portfolios is above the set of risk efficient individual investments. A) True B) False 4. What is portfolio return risk if rho = 0.7? A) 10% B) 9.22% C) 3.87% D) 70% 5. What is portfolio risk if rho = 1.00? A) 3.87% B) 0.00% C) 10% D) 5% 6. Assume rho = 0. What is the expected cash return if $125,000 is invested? A) $25,000 B) -$12,000 C) $15,000 D) $0.00 7. Assume rho = 0. What is sigma cash return (or cash risk) if $125,000 is invested? A) $2727 B) $4563 C) $125000 D) $8838 8. What is the portfolio risk if rho = -0.7? A) 3.87% B) 0.00% C) 4.27% D) 70% 9. (DO NOT NEED IMAGE FOR THIS ONE BUT YOU WILL NEED Z TABLE). A portfolio has an ECR of $17,000 and a Sigma cash return of $8,700, what is the probability that the portfolio will generate a cash return of more than $12,000 next year? A) 52.34% B) 0.00% C) 28.43% D) 71.57% 10. What is the expected return if the correlation coefficient (rho) between the investment returns is 0.7? A) 70% B) 10% C) 20% D) 0% \f1 Chapter 7: Risk Management 2 Risk and Return Risk averse investors Overweight negative outcomes compared to positive outcomes when making decisions If two investments have the same return RA investor prefers investment with lower risk If two investments have the same risk RA investor prefers investment with higher return Looking at chart Why does A dominate C? Why does A dominate B? Does A dominate G? 3 Risk Efficient Set of Investments 12 J K H 10 G 8 Profit D 6 F A E B 4 I C L 2 0 0 0.5 1 1.5 2 2.5 Risk 3 3.5 4 4.5 5 4 Other Investments on Chart What about K? What about f? What about lottery tickets? 5 Sources of Risk 1. Production and yield risk Very important at producer level 2. Market and price risk Input and output prices can be volatile Hedging with futures, forwards and options 3. Losses from disasters Very important in certain ag enterprises 4. Legal/political risk 5. Management risks 6. Technological change and obsolescence risk 6 Approaches to Managing Risk Hedging Price (source 2) futures, forwards, and options Cover in Ag Bm 320 and 420 Does not help with yield risk Hedging yield and disasters (sources 1 and 3) Insurance Cover in 407 How else can we manage risk? diversification!!!!!! 7 Diversification Why pick only one investment? We can invest in multiple enterprises Invest some wealth in growing corn and some wealth in milking cows Invest some wealth in growing soybeans and some wealth in growing corn invest some wealth in producing grape juice and some wealth in producing cranberry juice invest some wealth in making chocolate and some wealth in a theme park Diversification is one of the most important risk management tools Can help in hedging yield and price risk 8 Individual Investments v. Portfolios Portfolios will allow us to invest in COMBINATIONS of the individual investments and create an efficient portfolio frontier The efficient portfolio frontier is above the efficient frontier of individual investments 9 Risk Efficient Set of Portfolios 12 Risk Efficient Set of Portfolios J H 10 G Risk Efficient Set of Investments 8 Profit D 6 F A E B 4 I C L2 0 0 0.5 1 1.5 2 2.5 Risk 3 3.5 4 4.5 5 10 Profit and Risk Profit Can look at actual profit Measured in $ Can look at return on investment Measured in % Risk is a little trickier Standard deviation of profit Measured in $ Standard deviation of returns Measured in % 11 Portfolio Model A portfolio is a collection of investments Investor invests some of their wealth into multiple enterprises Livestock and grain corn and soybeans chocolate and theme parks Today we will focus on two portfolio examples 12 Two Investment Portfolio Investment 1 r1: expected return of investment 1 1: standard deviation of returns investment 1 w1: proportion of wealth invested in investment 1 Investment 2 r2: expected return of investment 2 2: standard deviation of investment 2 w2: proportion of wealth invested in investment 2 Portfolio Return rt = r1 w1 + r2 w2 13 Portfolio Return Example Investment 1: invest in a corn farm in Iowa r1 = 20% w1 = 50% Investment 2: invest in a corn farm in Nebraska r2 = 20% w2 = 50% Portfolio Return? 0.2*0.5+0.2*0.5 = 0.2 or 20% 14 What about risk? 15 16 17 Why diversify? 18 Back to Example Investment 1: invest in a corn farm in Iowa r1 = 20% 1 = 10% w1 = 50% Investment 2: invest in a corn farm in Nebraska r2 = 20% 2 = 10% w2 = 50% Seem like identical investments We have invested equally in both 19 Handout r1 r2 1 2 w1 w2 rho 0 -1 Value 0.20 0.20 0.10 0.10 0.50 0.50 rt Value2 na na 0.01 0.01 0.25 0.25 t Effect of Diversification 20 Effects of Diversification 21 What can manager control? 22 Expected Cash Return Suppose you invest $50,000 of E and $50,000 of D A = $100,000 Investment Alpha ra = 10% a = 10% wa = 70% Investment Beta rb = 12% b = 12% wb = 30% a,b = 0.5 23 Expected Cash Risk Investment Alpha ra = 10% a = 10% wa = 70% Investment Beta rb = 12% b = 12% wb = 30% a,b = 0.5 t =[0.12 *0.72+0.122 *0.32+2*0.7*0.3*0.5*0.1*0.12]0.5 24 Probability of a Cash Loss 25 Using z scores Z range Pr(value = target) z>0 1 - table probability table probability z $23,000 Pr(CR > 23,000) 29 Deep Thoughts: Gambling Versus Investing Gamble Heads I give you $-1.00 Tails I give you $2.00 We KNOW the probability of a heads is 0.5 We KNOW the probability of a tails is 0.5 We KNOW ECR and CR ECR = 0.5*-1 + 0.5*2 = 0.5 CR = 1.5 Investment $100,000 in a beef cattle business 30 Deep Thoughts: Calculating r and ? Two ways of approaching risky investments Statistical approach: collect historical data and compute historical return and historical 1. o More 'scientific' o assumes what happened in the past applies to the future o not always true Dead Reckoning: Allow for optimistic, most likely, and pessimistic outcomes and assign probabilities based on experience (guessing?) 2. o Less 'scientific' o look at this issue later in the semester when we study expected net present value 31 Deep Thoughts: Risk v. Uncertainty Risk: Know possible outcomes and probabilities, you can compute a true r and Most gambles know the probabilities/distribution Uncertainty: Don't know the probabilities of the possible outcomes. Need to use historical data or subjective probabilities to estimate and r Does history always repeat itself? All we really have are proxies for and r Most people use the terms 'risk' and 'uncertainty' interchangeably (fine for this class)