Answer to Question #55811 in Finance for Natalie




 A trader creates a long butterfly spread from options with strike prices $60, $65, and $70 by trading a total of 400 options. The options are worth $11, $14, and $18. What is the maximum net gain (after the cost of the options is taken into account)? Show all working in detail including the strategy, cost and payoff of the options and total payoff.
When the strike price is $60: the net gain is NG = (60 - 11)*400 = $19,600  
When the strike price is $65: the net gain is NG = (65 - 14)*400 = $20,400  
When the strike price is $70: the net gain is NG = (70 - 18)*400 = $20,800  
So, the highest net gain is $20,800 when the strike price is 70$.
1. the expected pay-out on each policy is 250 * 1/90 + 12000 * 1/100 + 17000 * 1/400 = $165.  so that's what the premium would have to be in order to get a profit of 0.
 
2. the profit per policy is the premium the company receives minus the expected payout = 350 - 165 = $185.
 
3. the expected profit on 375 policies would be 375 * 185 = $69375 this is a type of problem called linear programming. you'll want to first define your variables:
 
x = number of motorcycles made
y = number of bikes made
 
 
 
then, write equations that bound your problem:
 
0 ≤ x ≤ 100    (you can't make more than 100 or fewer than 0 motorcycles)
0 ≤ y ≤ 250    (you can't make more than 250 or fewer than 0 bikes)
x + y ≤ 300    (you can't make more than 300 vehicles total)
 
 
 
now, plot those equations and find the region of intersection. the region should be some enclosed polygon where all the equations are true. so:
 
draw vertical lines at x = 0 and x = 100. the first equation is true between those lines.
 
draw horizontal lines at y = 0 and y = 250. the second equation is true between those lines.
 
draw a diagonal line at y = -x + 300. the third equation is true below that line.
 
the enclosed region is a pentagon, with one side formed by each of the five lines.
 
 
 
now, find the vertices of the region of intersection. since yours is a pentagon, you'll want to find five vertices. some are straightforward:
 
x = 0 and y = 0 intersect at (0, 0)
x = 0 and y = 250 intersect at (0, 250)
x = 100 and y = 0 intersect at (100, 0)
 
some are slightly less straightforward:
 
y = -x + 300 and x = 100 intersect where y = -100 + 300. that's (100, 200)
y = -x + 300 and y = 250 intersect where 250 = -x + 300, or -x = -50, or x = 50. that's (50, 250)
 
so, the five points of intersection are (0, 0), (0, 250), (100, 0), (100, 200), and (50, 250).
 
 
 
now, write an equation for profit, p:
 
p = 1220x + 380y
 
this equation will have its maximum value (and its minimum value) at one of those vertices. plug each vertex in to figure out which gives you the maximum profit:
 
p = 1220(0) + 380(0) = 0 + 0 = $0
p = 1220(0) + 380(250) = 0 + 95000 = $95,000
p = 1220(100) + 380(0) = 122000 + 0 = $122,000
p = 1220(100) + 380(200) = 122000 + 76000 = $198,000
p = 1220(50) + 380(250) = 61000 + 95000 = $156,000
 
your maximum profit is $198,000, at 100 motorcycles and 200 bikes. of three numbers, second is twice the first and is also thrice the third. if the average of the three numbers is 44, the largest number is:

option 1) 24                              option 2) 56option 3) 72               option 4) 108option 5)    36 solution: in a given data, the highest frequency is 41, which lies in the interval 1000-15000.   
 here, l=10000, `f\_(m)=41=26, f\_(2)=16 and h=5000`   
 `"mode""=l+(f\_(m)-f\_(1))/(2f\_(m)-f\_(1)-f\_(2))xxh`   
 `=1000+((41-26)/(2xx41-26-16))xx5000`   
 `=1000+((15)/(82-42))xx5000`   
 `=1000+((15)/(40))xx5000`   
 `=1000+15xx125=10000+1875=11875`   
 hence, the modal income is 11875. Total no. of possible outcomes = 30 {1, 2, 3, … 30}  

  

E ⟶ event of getting no. divisible by 3.  

  

No. of favourable outcomes = 10 {3, 6, 9, 12, 15, 18, 21, 24, 27, 30}  

  

Probability, P(E) = (No.of favorable outcomes)/(Total no.of possible outcomes)  

  

P(E) = 10/30 = 1/3  

  

Bar E ⟶ event of getting no. not divisible by 3.  

  

P(Bar E) = 1 – P(E)  

  

= 1 - 1/3 = 2/3 hi,

lots of great explanations below, but i fear they might be difficult to truly conceptualize. 

let's start with a pie!

if there's a pie in front of us, that is the market. we'll call it 100 units of pie

we cut the pie in half - one piece (50 pie units) for you, and one piece (50 pie units) for me

scenario 1: we do nothing, we both have 50% market share.

scenario 2: i eat half my pie. my pie slice is now 25 units, yours is still 50 units. as a result, you have 67% of the market share and i have 33%. my "revenues" have fallen and my market share has fallen. your revenues haven't changed but you've gained market share

scenario 3: not only do i eat half my pie, but you also eat 20% of yours. still, i ate more, so even though your "revenues" are down, you've still gained market share.

scenario 4: we both get given more pie (yay). but, i get a whole other 50 units, and you only get 5 more. your "revenues" are up, but you've still lost market share!

i've created the below image for you to visualize this better (click on it to blow it up)...hope this helps! 1.i made my ( ) buying and selling stocks (1.wealthy 2.fortune 3.treasure)

2.in team sports, how all members work as a group is more important than how they perform ( ) (1.frequently 2.completely 3.individually 4.typically)

3.the professor did his best to ( )the students with new ideas.
 (1.display 2.witness 3.review 4.acquaint )

4.i made my ( ) buying and selling stocks. (1.wealthy 2.fortune 3.treasuer)

5.there isn't ( ) beef in the kitchen. (1.some 2.many 3.two 4.any )

6.last friday ( )my sister's birthday,and she had a good time.
 (1.had 2.is 3.was 4.has)

7.the students started ( ) the park, and rode their bicycles along the road,
 (1.from 2.in 3.at 4.to )

8.younger sister who will help me with my homework after you go abroad for studies?
older sister ( )
younger sister: i don't know if it will be enough.
(1.your classmates all need to do their homework too. 
2.the teacher will want you to turn your assignments in on time.
3.mom and dad can't afford to hire a tutor,
4.just do your best amd you'll be fine .)

9.my recent trip to europe has left a ( ) impression on me.
( 1.forever 2.final 3.lasting 4.long)

10.any assets that can be used to make immediate payments are comsidered.
(1.indemnity 2.liquidity 3.liability 4.stock)

11.how much ( ) did she have last night?
(1.books 2.pens 3.homework 4.cats)

12.all of us must have the ( ) that there is no free lunch.
(1.know-how 2.dispute 3.wonder 4.awareness )

13.today is those ( ) birthday.
(1.a gril 2.girl 3.girl's 4.girls' )

14.these two photographs are too small. let's have them ( )
(1.formalized 2.increased 3.expanded 4.enlarged ) that is still 135 more than i'd pay you. given that,l ‖ m and n cuts themlet,∠1 = 65o∠2 = x∠3 = 40o∠1 = ∠4 = 65o (alternate angle) (i)∠3 + ∠4 + ∠5 = 180o (angle sum property)40o + 65o + ∠5 = 180o∠5 = 75onow,∠2 + ∠5 = 180o (linear pair)x + 75o = 180ox = 105o statement of profit or loss