Visualization of Macaulay duration as a point of total immunization

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• A Numerical Example

In this section we consider a basic numerical immunization example. Suppose you are trying to immunize a year-10 obligation whose present value is $1,000; that is, at the current interest rate of 6 percent, its future value is: $1,000[pic][pic]= $1,790.85 You intend to immunize the obligation by purchasing $1,000 worth of a bond or a combination of bonds. You consider three bonds:

i. Bond 1 has 10 years until maturity, a coupon rate of 6.7 percent, and a face value of $1,000. ii. Bond 2 has 15 years until maturity, a coupon rate of 6.988 percent, and a face value of $1,000. iii. Bond 3 has 30 years until maturity, a coupon rate of 5.9 percent and a face value of $1,000.

[pic]
If the yield to maturity doesn’t change, then you will be able to reinvest each coupon at 6 percent. [pic]

The upshot of this table is that purchasing $1,000 of any of the three bonds will provide—10 years from now—funding for your future obligation of $1,790.85, provided the market interest rate of 6 percent doesn’t change.

Now suppose that, immediately after you purchase the bonds, the yield to maturity changes to some new value and stays there. This change will obviously affect the calculation we just did. For example, if the yield falls to 5 percent, the table will now look as follows:

[pic]

Thus, if the yield falls, bond 1 will no longer fund our obligation, whereas bond 3 will overfund it. Bond 2’s ability to fund the obligation—not surprisingly, in view of the fact that its duration is exactly 10 years—hardly changes.

...witnesses, actuarial tables are acceptable evidence to show life expectancy. Juries may award damages(money) to plaintiffs (person who is suing the defendant) for compromised life expectancy resulting from the alleged crime of the defendant.
An actuarial valuation is a type of appraisal (official valuation) which requires making economic and demographic (structure of population) assumptions in order to estimate future liabilities (being responsible for). The assumptions are usually based on a mix of statistical tables and experienced judgment. Because assumptions are often derived (obtained) from long-term data. Unusual short-term circumstances or unanticipated trends can occasionally cause problems. A common example where an actuary directly affects someone’s personal life is in the valuation of a pension fund. It is usually easy to value the assets of a pension fund because it primarily holds liquid (accessible) securities such as stocks or bonds because it is just a mathematical valuation. However, it can be very difficult to value the liabilities of a pension fund, because assumptions must be made to determine the total value of pension payouts that must be made in the future. Assumptions must also be made as to the expected growth of the fund's assets (properties) which will allow it to meet those obligations. If either set of assumptions proves to be significantly wrong then there might be too little (or too much) funds in...

...UNIVERSITY OF CAPE TOWN
NOVEMBER 2009 EXAMINATIONS
INTRODUCTION TO ACTUARIALSCIENCE (BUS1003H)
Time allowed: 2 hours Total marks: 70
INSTRUCTIONS
• Answer all questions
• You must show your working in full in all questions
• Approved calculators may be used, but all memories and user-supplied programmes must be cleared before you begin the examination.
• Some tables are provided.
• For each of the multiple choice questions write down exactly one of the symbols A,B,C or D to indicate which of the suggested answers you think is most correct.
• Marks shown are approximate.
• The Question Paper is in 8 parts. Answer each part in a separate answer book.
PART 1 consists of questions 1- 22 These should go into a separate book. (SK)
PART 2 consists of question 1 This should go into a separate book. (SR)
PART 3 consists of questions 1-2 These should go into a separate book. (HdT)
PART 4 consists of question 1 This should go into a separate book (MV).
PART 5 consists of questions 1-2 These should go into a separate book. (SK)
PART 6 consists of question 1 This should go into a separate book. (RD)
PART 7 consists of question 1 This should go into a separate book. (IM)
PART 8 consists of question 1 This should...

...ASSIGNMENT
UDBS
Consider a 10 year bond that has a face value shs 1000, a coupon rate of 6% and pays interest once a year.
(a)Suppose person A bought this bond at par when it was initially issued and sold it 1 year later to person B for shs 1024.What is B’s total return?
Soln
Total return =[ Interest paid +(selling price – buying price)]/buying price
Given; Annual interest paid = coupon rate x par value, coupon rate = 6%, par value =1000.
= 6% x1000
=60 , buying price = 1000, selling price = 1030
,
= [60 + (1030 – 1000 )]/1000
=0.09 or 9%
(b)Suppose B holds the bond for 1 year and sells it to person C for shs 1024.What is B’s total return?
Soln
Given; annual interest paid = 60, buying price = 1030, selling price = 1024
=[60 + (1024 – 1030)]/1030
=0.052 or 5.2%
(c)Assume C holds the bond for 3years.Suppose that at the end of these 3 years market interest rate for bonds similar to this one is 7%
i)What price should C expect to fetch in the market?
VB =INT(1 -1/(1 + rd)n /rd ) + m/(1 +rd )n
Given; INT = 60, rd =7%, n = 5, M = 1000.
= 60(4.1) + 713
=246 + 713...

...BOND PROBLEM SOLUTIONS
1. Six years ago, The Corzine Company sold a 20-year bond issue with a 14 percent annual coupon rate and a 9 percent call premium. Today, Corzine called the bonds. The bonds originally were sold at their face value of $1,000. Compute the realized rate of return for investors who purchased the bonds when they were issued and who surrender them today in exchange for the call price.
PV = 1000; N = 6; PMT = 140; FV = 1090; CPT I/Y
I/Y = 15.02%
2. You just purchased a bond which matures in 5 years. The bond has a face value of $1,000, and has an 8 percent annual coupon. The bond has a current yield of 8.21 percent. What is the bond’s yield to maturity?
CURRENT YIELD = ANNUAL COUPON ( PV
0.0821 = 80 ( PV
PV = 80 ( 0.0821 = 974.42
N = 5; PMT = 80; FV=1000; PV = 974.42 CPT I/Y
I/Y = 8.65%
3. The Dass Company’s bonds have 4 years remaining to maturity. Interest is paid annually; the bonds have a $1,000 par value; and the coupon interest rate is 9 percent. What is the yield to maturity at a current market price of $829? Would you pay $829 for one of these bonds if you thought that the appropriate rate of return was 12 percent?
PV = 829; N = 4; FV = 1000; PMT =90; CPT I/Y
I/Y = 14.99%
YES, IF YOU THOUGHT THE APPROPRIATE RATE WAS 12%, YOUR PV WOULD...

...perpetual bond is currently selling for RS. 95/-. The coupon rate of interest is 13.5%. The approximate discount rate is 15%. The value of the bond and the YTM is:
(a) Rs. 90/- and 14.2% Value is (13.5*15%=90) and YTM is ((13.5/95)*100=14.21%)
(b) Rs. 100/- and 13.5%
(c) Rs. 90 and 15%
(d) Rs. 90/- and 13.5%
902. In 2001, Meridian Ltd. has issued bonds of Rs. 10,000/-each due in 2011 with a 14% per annum coupon rate payable at the end of each year during the life of the bond. If the required rate of interest is 8%, find the present value of the bond. Tick the nearest option.
(a) 10,000
(b) 7302
(c) 2,700
(d) 14,026 (9394.11+4631.93=14026.05)
903. The present market value of an equity share is Rs. 80/-; and the exercisable price of the warrant is Rs. 60/- per share. An investor is holding a warrant entitling him to purchase 50 equity shares. The minimum value of the warrant is:
(a) 1,000/- (80-60=20*50=1000)
(b) 4,000/-
(c) 3,000/-
(d) None of these
904. A bond with a coupon rate of 8% is available at its face value of Rs. 1,000/-. The market rate of return on an instrument with similar risk goes down to 6%. The bond price will become:
(a) 1,000/-
(b) 750/-
(c) 1,333/- (800/6%)
(d) None of these
905. A bond with a coupon rate of 10% is available at Rs. 1,250/-. The face value of the bond is Rs. 1,000/-. The...

...ActuarialScience applies mathematical, statistical, financial an economic theory to solve real problems arising in applied subjects such as commerce, governments, insurance and banking, typically involving risk, uncertainty, and the financial impact of certain events.
The BSc in ActuarialScience and Mathematics is accredited by the Institute and Faculty of Actuaries. The course gives a firm foundation in Mathematics, together with specialist course units in ActuarialScience whilst giving you the opportunity to develop team working, communication and leadership skills.
Every area of business is subject to risks so an actuarial career offers many options. A typical business problem might involve analysing future financial events, especially when elements are uncertain. But it could also involve understanding something like the weather: assessing when and where devastating storms may hit and their associated costs, for investments or insurance. Due to an actuary's skill the opportunities open to them are endless, they can even be employed in the marketing and development of financial products.
Understanding how businesses operate is vital, but what really set actuaries apart are their natural mathematical, economic and statistical awareness, and their ability to apply this to real business issues. The ability to communicate these difficult topics to non-specialists is also...

...IEOR 221 - Spring 2014
Immunization Notes
February 13, 2014
1
Assumptions
The risk-free interest rate is 9%. The following bonds (with face value $100 and same
YTMs are also available on the market:
Bond 1
Bond 2
Bond 3
2
Coupon Rate
6%
11%
9%
Maturity
30 years
10 years
20 years
Price
Yield Duration
$69.18 9%
11.8809
$112.84 9%
6.745
$100.00 9%
9.9501
Setting
Groupon has an obligation to pay $1 million in 10 years. The president of Groupon sets
aside $1million = $422, 410.801, and asks you to put in the bank, which is earning 9% per
1.0910
year. His argument is that by year 10, this will grow to $1 million, allowing the company to
pay oﬀ the debt.
1. Is this a sound approach? What would go wrong?
2. Everything is ﬁne if the interest rate stays at 9% throughtout the 10-year period.
Otherwise, we will either have more than 1 million in year 10 (which is the favorable
scenario, everyone will be happy), or less than 1 million in year 10.
3. As an example, suppose interest rate stays at 9% for the ﬁrst 3 years, but changes to
8% in the 4th year, and stays the same thereafter. The value of the investment in year
10 is going to be
422, 410.81 × 1.093 × 1.087 = 937, 520.57 < 1million
4. Suppose we want stability. That is, we want to be able to pay oﬀ the $ 1million
obligation in 10 years, no matter how th einterest rate (yields) changes (assuming if...

...
We need Immunization
In the past we have had several different types of deadly diseases, such as: Hepatitis, Influenza, and Tetanus. Many people have died because of this. Luckily humans have figured out ways to defeat these epidemics and prevent them from happening again. In order to completely get rid of these diseases everyone needs to take these vaccinations. The thing is it cost money to produce and receive the vaccine. According to the “Report of the Joyce Foundation Special Project on immunization” most of the reason why children aren’t getting properly vaccinated is because of financial problems or not being educated enough. This institution found that there was five ways to increase the immunization rates. Educating health care providers to improve the immunization records in their communities. They said Increasing the access of vaccines would also help out a lot. Educating parents about the costs and effects of immunization lets them realize the effects of their children not getting vaccinated. Another thing was to improve the vaccination services. Last thing was to set out campaigns to raise money and awareness about vaccinations.
Most people probably do not think about the importance of these vaccines, when in fact these vaccines save lives. Luckily it is law that before children can start school that they have to have a certain vaccines before they are allowed in the...