A bank offers a $100 certificate which redeems a variable amount after 5 years c
ID: 2383444 • Letter: A
Question
A bank offers a $100 certificate which redeems a variable amount after 5 years calculated as follows: $108and: $+1.08 for every percent that XYZ index went up, or: -$1.08 for every percent that XYZ index went down. For example, if XYZ index goes up 10% over 5 years, the certificate reddems 108+1.08*10= 118.80. If XYZ index goes down 5%, the certificate redeems 108-1.08*5=102.6. Note that fractions of percentage points are allowed, and that the certificate may redeem less than $100.
Q: a. draw the redemption amount of the certificate as function of index performance(percentage change) PLZ indicate all remarkable values on your axes.
b. In what market scenario would the certificate redeem $120? what is the corresponding annualized return on investment(with annual compounding)?
c. what is the max theoretical loss on the certificate ?
d. using the infomation below calculate the profit made by the bank on each $100 certificate. plz show and explain. - the IR is 5% p.a, i.e a $1 deposit grows to $1.05 after one year. - The current price of XYZ index is 20$ - The 5-year forward price of XYZ index is $21.60.
Explanation / Answer
Q.b. ANSWER is if the market [i.e. XYZ Index value] goes up 11.11%, the certificate would redeem $120.
Substituting the given values in the formula:
108 + (1.08*x)= 120; we solve for x to obtain answer as 11.11%..
The instrument (i.e Bank Certificate) of $100 yields $120 after 5 years; thus if we apply annual compounding formula, we get:
(120 / 100)= [(1+r / 100)5]
1.20= [(1+r / 100)5]
Thus, solving for "r" in MS Excel Spreadsheet using iteration function, we get:
r= 3.72% per annum; annually compounded .......... ANSWER
Q.c.
Redemption amount on bank certificate=[108-(1.08*100)]= 0 ==> Redemption amount after 5 years if XYZ Index gets completely eroded to zero in this period.
The maximum theoritical loss on the bank certificate can be = entire $100.
Logically,
Entire $100 + Opportunity Cost of Capital [expected annual return] for an equally risky investment available in the market for 5 years, is the total loss on bank certificate investement, in this worst scenario of XYZ Index fall.
Q.d.
The ANSWER is that the bank makes profit of $10.98816 on each $100 certificate; Explainationas follows:
Given the 5-year forward XYS Index Vaue i.e. 5-year forward price of $21.60 and its current price of $20.00, the totsal return on XYZ Index over 5-year period would be= 8% i.e. 21.60 / 20.00= 1.08, which means $8 on each $100 of investment in the XYZ Index over 5-year period..
The redemption amount of the bank certificate corresponding to this forward Index Value= 108 + (1.08*8)= $116.64
As against this, the total compunded value of each $100 bank deposit through issuance of bank certificate= 100*((1+0.05)5)= $127.6282;
Thus, after 5-year period, bank will have to redeem $116.64 against grown compunded deposit value of $127.6282; thereby making a profit of $10.98816 each $100 Certificate.. [ANSWER]
Q.a. Am unable to draw the Redemption function of $100 Bank Certificate because the CodeCogs Equation Editor i.e. fx [i.e. function menu in the tool bar] is not properly working.. There is some technical problem with this menu as of now.
However, to guide,
Draw two axes i.e. X-axis and Y-axis;
Then assign different regular-interval values of XYZ Index Performance [i.e. Percentage Change] to X-axis
and assign different regular-interval values [possible outcome values] of Redemption amount on Bank Certificate to Y-axis.
Then plot different points in the two-axes zone basis the linear equation:Redemption Amount, y= $108+ 1.08 (x) for different values of x and y
Then join all these points by a line to obtain the Redemption Amount function curve. Thus you will be able to obtain your answer by following the above guiding steps..