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Economics 434
Financial Markets
Professor Burton
University of Virginia
Fall 2015
November 3, 2015
Duration – One More Time
• Pure Definition: (dP/dy)/P
– Percentage drop in value of bond for a small
increase in yield
• But McCauley Duration is: weighted average
of maturities of payments where the weights
are the fraction of present value that is
embodied in that specific payment with the
specific maturity
November 3, 2015
Continuing
C
C
C  Pr incipal
P

 ........ 
2
1  y 1  y
1  yn
dP ( 1) * C ( 2) * C
(  n) * C  Pr incipal 


 ..... 
2
3
n1
dy 1  y 
1  y
1  y
Rearranging gives:
dP  1   1* C
2*C
n * C  Pr incipal 
 * 

 

 ... 

2
n




dy  1  y   1  y 1  y 
1  y 

P
Economics 434 – Financial Market Theory
P
Tuesday, Oct 20, 2015
Duration Equals McCauley Duration for a
treasury bond or note
dP  1   1* C
2*C
n * C  Pr incipal 
 * 

 

 ... 

2
n




dy  1  y   1  y 1  y 
1  y 

P
P
Duration
McCauley Duration
1
1  y 
Is approximately equal to 1
Duration Equals McCauley Duration for a
treasury bond or note
dP  1   1* C
2*C
n * C  Pr incipal 
 * 

 

 ... 

2
n




dy  1  y   1  y 1  y 
1  y 

P
P
Duration
McCauley Duration
1
1  y 
Is approximately equal to 1
Example, Recent 2 Year Note
• Coupon 5/8
– Means payments twice yearly of 5/8 divided by 2
multiplied by $ 1,000 = $ 312.50
Current Price = Present Value =
312.50
1+𝑟
+
312.50
1+𝑟 2
+
312.50
1+𝑟 3
+
100,312.50
1+𝑟 4
312.50
𝑤1 = 𝑊𝑒𝑖𝑔ℎ𝑡 𝑜𝑓Type equation here.𝑓𝑖𝑟𝑠𝑡 𝑐𝑜𝑢𝑝𝑜𝑛 =
1+𝑟
divided by P
100,312.50
1+𝑟 4
divided by P
W4 𝑊𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑓𝑖𝑛𝑎𝑙 𝑐𝑜𝑢𝑝𝑜𝑛 𝑎𝑛𝑑 𝑝𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 =
McCauley Duration is = 1 times w1 plus 2 times w2 plus 3 times w3 plus 4 times w4
November 3, 2015
Meanwhile Back to ABS
• Broad principles
– Create a pool of fixed income securities (or could
be bank loans)…debt instruments generally
– Using the pool’s cash flows, create brand new
securities with usually a wide range of credit
quality
• New securities created are driven by demand
for certain credit qualities and durations
(where such combinations may not be
currently available)
November 3, 2015
November 3, 2015