# Q Methods!!

An investor wants to buy a condominium. The value of her portfolio is current \$1m and she needs \$100,000 in one year for the down payment. She doesn’t mind decreasing her capital as long as she has \$950,000 remaining in her portfolio after the down payment is made. She is considering two new portfolios for her holdings. The details on the two portfolios are: Port 1 - Exp. return: 17% Standard dev. 15% Port 2 - Exp. return: 12% Standard dev. 10% Using roy’s safety first criterion, what portfolio would she prefer and what’s the probability this portfolio would produce a return less than 2%: any idea??

so you got 150k negative loss acceptable. her risk free return is essential 10000/1mil = 10% so for A 17-10/15 = 7/15 = .5 approx for B 2/10 =.2 prefer portfolio A. annd p ( X < 2) = standarize -2-17/15 = -1.80 zscore of -1.8, find the area under it. guessgin approx 8%? sound swrong. gotta be more…

she needs 5% return (a.k.a an addition of \$50,000 to her \$1,000,000) roy’s safety first ratio with 5% target A: (17-5)/15 = 0.8 B: (12-5)/10 = 0.7 A is the better portfolio because it has a higher safety first ratio… now you want to find the probability of portfolio A going below 2% find z=(2-17/15) = -1 P(Z1) = 1-P(Z<1) =1-0.8413 =15.87%

Roy’s safety first is just as the Sharpe ratio, except instead of Rf you have the target return. Portfolio 1: (17%-2%)/15%=1 Portfolio 1: (12%-2%)/10%=1 Both portfolios have the same Roy’s safety first criterion, but given the higher variability of Portfolio 1, the safer one would be Portfolio 2. The probability of a retun of less than 2% is given by that’s to the left of the 2% under the cummulative probability, and that would be for a Z score of (12-2)/10=1, look up a table of cummulative probabilities, greater than 2% would be 84.13%, that means 1-84.13% is lower, your probability is 15.87. Are these the answers?

Amd I was wrong again:) forgot about the need for 50,000!!!

Does not mind portfolio falling below 950, and wants 100K out of a 1000K portfolio. So she needs return of at least 50K on her 1000K portfolio to be able to pay the down payment. rf = 50 / 1000 = 5% Port 1: Safety first criterion: (17-5)/15 = 0.8 Port 2: SF Criterion: (12 - 5) / 10 = 0.7 So Port 1 should be selected. Probability this port will produce a return < 2 (2 - 17) / 15 = -1 --> 16% Ans.

you and sharp are right. reading too fast here.

good job !!! that’s the answer!

potfolio A, 16%

I am missing samething here cpk123. You say the investor does not mind portfolio falling below 950, but doesnt it say “she doesnt mind dicreasing her capital as long as she has 150K remaining in her portfolio after the down payment is maid”?? and after the down payment is maid she is going to have just 900K, and not 950…

Edit: The question clearly says: She doesn’t mind decreasing her capital as long as she has \$950,000 remaining in her portfolio after the down payment is made. So you are reading something which is not given in the question End Edit the portfolio cannot fall below 950K – given. Needs 100K to make down payment. So needs at least 50K on the 1M portfolio to be able to use 50K out of the portfolio + 50K gained on the portfolio. so rf = 50/1000 = 5% Hope that makes sense.

Yes, makes sense.

> now you want to find the probability of portfolio > A going below 2% > > find z=(2-17/15) = -1 > > P(Z1) = 1-P(Z<1) > > =1-0.8413 > > =15.87% if you want the prob of A going below 2, wouldn’t you do -2 -17 / 15 = -19/15 = -1.266 and then look up the area to the left of that on the normal distribution?

why -2??? you need probability of it going below +2… as asked in the question. CP

ok. today i am starting out on 5 wrong out of 5 attempted morning!!!