Smart People: Help me do math homework
 

How would a person begin to answer this problem?

If I could, I would.

but since I can't....

Poop.

Would you not have to know the amount to be invested first?

Investing in 50% of the 8.5%, 20% of the 9.2 and 30% of the 3.1 would give you a 6.82% projected return....is that what you're after?

Well, we can make up any number. Let's say I have $100K.

Don't forget to carry the naught.
Sec

Mostly I'm trying to figure out how you came up with that answer, and how I can come up with other answers.

Unless this is multiple choice or there are at least three more constraints (equations), I'm pretty sure there is more than one solution to this problem. As it is, this is all we have to work with:

A(1.085)+B(1.092)+C(1.031)+D(1.048)=1.065

That's right, there are infinite number of solutions. I want to put together at least 5 options.

Yeah, I guess that was not relevant.....I should have left it to the smart people.

Cheater!

So now I just get to plug in numbers for A, B, C, and D?

Okay, then go to this website and go wild filling in the letters in the equation I included.

ROFL

Yep. If you want a discrete solution, fill in 3 of them and leave the fourth as a variable, and Wolfram will calculate it.

Hell, maybe I'm oversimplifying it (aka completely ****ing it up)

How does it feel to be smart? Is it a burden at times?

this!:)

There are multiple solutions, but a mix of:

1 - 0.575262544
2 - 0
3 - 0.252042008
4 - 0.172695448

Gives an ER of 0.065.


Solver is your friend. You have 4 unknowns, 2 equations, and conditions on the 4 unknowns.

Did you figure that out doing the A(1.085)+B(1.092)+C(1.031)+D(1.048)=1.065 or did you use another method?

That's the formula for expected return (you can also use the same formulat without the leading 1's, i.e. A(0.085) + B(0.092)...) and 1 of your two equations.

Your 2nd equation is A + B + C + D = 1.

You can use a mix of Investment 1 & I3 or I4 then a mix of I2 plus I3 or I4. That gives you 4 mixes. You can combine any of those solutions to make a fifth.
Use xI1 + (1-x)I3=.65 solve for x.

Substitute any 2 investment options above and below target.

It's just a question of weighted averages. You must have at least one of the investments that are higher than 6.5 and at least one of the investments that are less than 6.5. To actually solve this you need more information about total dollars invested, the maximum number of individual investments that can be made or a ratio of dollars invested between funds.

If you just average your 4 percentages, you are close to begin with at 6.4%.

So let's say you invest $4000.

25%, or $1000, at each of the 4 rates....

1000 at 8.5% = 85.00
1000 at 9.2% = 92.00
1000 at 3.1% = 31.00
1000 at 4.8% = 48.00

for a total of 256.00.

256.00/4000 = .064 = 6.4%

260.00/4000 = .065 = 6.5%

So therefore you need to find a way to get $4.00 more back on you investment.

I'm going to use the 9.2% and the 4.8% and the 1000.00 at each rate

We made 140 dollars at those two rates combined. We need 144 dollars to get to 260 dollars.

X = amount invested at 9.2%
2000 - X = amount invested at 4.8%

.092X + .048(2000 - X) = 144.00
.092X + 96.00 - .048X = 144.00
.044X = 144.00 - 96.00
.044X = 48.00
X = 48.00/.044
X = 1090.91


2000 - 1090.91 = 909.09

What percent of 1000 is 1090.91?

109.1%

109.1% of your original investment, which was 25%, is

25 times 1.091 = 27.275

What percent of 1000 is 909.09?

90.9%

90.9% of you original investment, which was 25%, is

25 times .909 = 22.725

So, your your percentages to be invested at each rate to give you a 6.5% return...

25% of your money at 8.5%
25% of your money at 3.1%
27.275% of your money at 9.2%
22.725% of your money at 4.8%

This is just one solution, but it will work for any amount that you choose to invest.

reading through this thread makes me realize how stupid I am.

You're making this too hard. You don't have to blend all four. It's a lot easier to blend 2 and put it into a simple algebraic equation.

For example, you can use holdings 1 (x) and 3 (y).

x(8.5) + y(3.1) = 6.5% is your equation.

Now, you have to express x in terms of y. Because x+y= 100% (1.00) of your investment, x=1.00-y

Now, you re-write the equation with only the y variable:

(1-y)(8.5)+y(3.1)=6.5

Do the multiplication:

8.5-8.5y+3.1y=6.5

Simplify further

8.5-5.4y=6.5

Subtract 6.5 from both sides of the equation

2-5.4y=0

Add 5.4y to both sides

2=5.4y

Divide both sides by 5.4 to solve for y

.37=y

37% of your investment should be in y. The rest (1-y) should be in x.

Check your work: .37(.031)+.63(.085)=.065

Especially Coog and Saul Good. Give me a history book, and I'll have that subject mastered. Give me a few numbers, and I'll start to sweat.

Yikes.

no joke there.
my wifre is a wiz at math; but hates history.

I k now enough math do do my taxes and balance a checkbook.

The answer is....


4?

The answer you're looking for is:
Nicaragua

The answer is:

on Near RT Zip- Lucky 860 H Shoot Swing "zorro", your first progression is H, followed by Z and Y. If M OL, X is first read.

Just write "CASH RULES EVERYTHING AROUND ME CREAM GET THE MONEY DOLLAR DOLLAR BILL Y'AAAALLLLLL"

Cak'n padna?

My name is Leonard Cooper (formerly Leon Sandcastle) and my response is:

"Who is some guy in Normandy. But I just won $75,000!"

God I hated math, my worst subject.

La l,

I had to rush off this afternoon before I could really finish some details. Hope it makes more sense now. The solution I gave you is just one of many, but it will work for any amout of money that you would choose to invest.

Whatever you do, don't let the legbreakers find out you're skimming off the top.

This is a stupid problem. Why would you want less than the maximum expected rate of return?

Now a more interesting question would be to develop a portfolio that maximizes the rate of return while mitigating risk. To properly answer this question we would need to know the uncertainty or expected variance of each of the investments. Also, we need to know the extent to which the various holdings are correlated with one another. We could then present various portfolios match the career stage and risk tolerance of an individual investor. Do you have a problem like that?

You somewhat answered your own question: the risk necessary to earn a greater expected return may be too high for an investor. That is why, with the other information you mentioned, one would find the efficient frontier and invest at the defined level of risk. I'm certain whatever class this is for they are building up to that analysis.

Knowing La Lit, I'm pretty sure its not. He's a word geek, not a numbers geek.

Then I agree that it's a pointless assignment.

not 100% certain, but I think he used math.

That's all good if he is allowed to only use 2 of the 4 options. But if he is required to use all 4 of the percentages listed, he better go with something like along the lines I provided for him.

EDIT: We are essentially doing the same thing... I just eliminated 2 of the options by giving each a 25% value. Didn't mean to come across as my way was better Saul Good! Hope you didn't take it that way.

Ugh efficient frontier is such a flawed concept. They finally dropped it from the CFA curriculum.

Not saying your wrong, just nitpicking about my least favorite part of portfolio management theory in modern finance.

Thank you for that. In nearly every situation, you would be correct. However, I'm taking Wealth Management this semester in a foray back to undergrad classes. Being my last semester at law school, I can afford to take a relaxed schedule. I wanted to take this course (along with espanol) because I know that clients will ask me about the issues in estate planning, and I wanted to have some idea of good financial investment options. I'm really enjoying it so far, but the minor amount of math involved is an obstacle, unfortunately. I can figure out basic things like what savings total at retirement is necessary for a person who wants xK per year to live on, but aside from that, I'm a fish out of water.

It seems like each investment firm develops their own efficient frontier portfolio.

I hate to be an asshat, but given the limited amount of information you gave in the OP, it seems as if a few more thank you's besides the one you just gave would be in order.

Yes, thank you. Rep on the way. That was all the info I was given.

Turns out most students have some Solver program on Excel, which I've since added but have no idea how to use. So I'll probably be sticking with these formulas you and others have provided.

You're welcome! I realize the answer I gave you was pretty much basic algebra in step-by-step, but it will work for any amount of money you wish to invest.

Hope you get an A. :thumb:

It's cool that you are stretching yourself trying to develop a working knowledge of something out of your comfort zone. I've always wanted to learn to play guitar or piano (music doesn't come easy for me), but my hands seem to be the fastest aging part of my body, so that isn't happening.

If you have to use all four, simply divide the percentages in half, do the same thing for options 1 and 2, and add them together.

Standard algebra is really all that is needed here, and it's about a 30 second solution. I don't feel like math instructors do a good enough job of translating their teachings into practical applications. There really isn't any point in learning algebra if you don't know how to apply it. If you do, it's actually extremely useful and comes in handy a lot more often than most people probably realize.

Then, when you use it, people look at you like you just explained string theory even though you're just really busting out something you learned in 7th grade.