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Effective duration and Convexity of bonds
emlyn ngwiri
#1 Posted : Friday, August 13, 2010 10:18:31 AM
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Joined: 8/12/2010
Posts: 129
Location: nairobi
Morning guys,

i was reading the other day about the above topic and couldn't help ponder if infact the effective duration (sensitivity of a bonds price to changes in yeild)convexity and the term structure of interest rates are actually considered when pricing/valuing bonds in kenya? if so, do the annualized yields correlate to the one in europe considering the theories of the term structure? Think
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bonds_color-medallion-logo-no_bgrd.jpg (28kb) downloaded 6 time(s).
emlyn ngwiri
#2 Posted : Friday, August 13, 2010 12:03:40 PM
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Joined: 8/12/2010
Posts: 129
Location: nairobi
no replies guys? come on help me out?
kizee
#3 Posted : Friday, August 13, 2010 4:22:00 PM
Rank: Member

Joined: 1/9/2008
Posts: 537
emlyn ngwiri wrote:
Morning guys,

i was reading the other day about the above topic and couldn't help ponder if infact the effective duration (sensitivity of a bonds price to changes in yeild)convexity and the term structure of interest rates are actually considered when pricing/valuing bonds in kenya? if so, do the annualized yields correlate to the one in europe considering the theories of the term structure? Think


so ur askin if kes govt bond yields correlate to those of european bond yields? correlation implies a departure of 2 or more variables from independence...so are u askin whether the kes yield curve and the european bond yield curve are correlated ama? if thats ur question u wud have to do a correlation analysis..lucky for u i have a tool which i use for this..
Scooby
#4 Posted : Friday, August 13, 2010 4:25:09 PM
Rank: Member

Joined: 9/2/2006
Posts: 121
Hi Emyln,

I dont think the government does not use effective duration and convexity in the pricing of its bonds. In Kenya, the main determinants of interest rates are two - the liquidity in the market and how much the government wants to borrow.

What has been happening in Kenya for the past twelve months is that there has been higher levels of liquidity than is the norm. CBK has therefore taken advantage of that to reduce the level of interest rates for any bond that they offer.

The same concept does apply to other markets globally. The only difference is that other governments have to take into consideration, what the investors expect as interest if they want their auctions to be successful.
emlyn ngwiri
#5 Posted : Friday, August 13, 2010 4:53:34 PM
Rank: Member

Joined: 8/12/2010
Posts: 129
Location: nairobi
@Scooby indeed true bearing in mind the term structure theories of liquidity,preference,expectations and market segmentation, but the gist of my question is that we know that factors such as the type of issuer,taxability of interest,inclusion of options financability of the issue etc etc, all affect the term structure.... is it in order to say that lower duration means higher yield and vice versa and if so higher volatility implies lower yield to maturity?

@kizee ebu send me that link. i am asking if the annualized yields factoring in all elements that affect convexity (callability,yield curve etc affects or accounts for the inaccuracies of the linear duration line?
kizee
#6 Posted : Friday, August 13, 2010 5:39:48 PM
Rank: Member

Joined: 1/9/2008
Posts: 537
emlyn ngwiri wrote:
@Scooby indeed true bearing in mind the term structure theories of liquidity,preference,expectations and market segmentation, but the gist of my question is that we know that factors such as the type of issuer,taxability of interest,inclusion of options financability of the issue etc etc, all affect the term structure.... is it in order to say that lower duration means higher yield and vice versa and if so higher volatility implies lower yield to maturity?

@kizee ebu send me that link. i am asking if the annualized yields factoring in all elements that affect convexity (callability,yield curve etc affects or accounts for the inaccuracies of the linear duration line?




i tried pluggin in values for the euro and kes benchmarks and didnt get a result...sori cant help
Scooby
#7 Posted : Friday, August 13, 2010 7:20:35 PM
Rank: Member

Joined: 9/2/2006
Posts: 121
Hi Emyln,

A lower duration means that an investor has lesser concerns about interest rate risk (or in your words, lower interest rate volatility) and would therefore not mind getting a lower interest rate for their investment. The opposite is true for long duration.

The issue of yields is not influenced by the government or CBK. Thats a function of the secondary market. The high demand this year for treasury bonds has resulted in the market prices of bonds hitting the roof - thereby resulting in the significantly lower current yields (for you its yield to maturity).

As I mentioned, the government is taking advantage of that to price the current infrastructure bond at 6%. And in order to ensure that its fully taken up, they offered such incentives as tax free interest (as opposed to taxable interest).

As for type of issuer, government bonds are deemed to be risk free hence can offer a lower interest rate. If Housing Finance had also decided to issue a similar infrastructure bond, it would have been forced to charge a higher interest rate as they are deemed to be more risky that the government.

The market in Kenya is yet to fully adopt the impact of optionalities when pricing the bonds. The KenGen and ARM bonds should have charged a higher interest rate than what they were offered at. The use of options does affect the duration of a bond/portfolio.
emlyn ngwiri
#8 Posted : Saturday, August 14, 2010 12:05:26 PM
Rank: Member

Joined: 8/12/2010
Posts: 129
Location: nairobi
@scooby i tend to differ on the issue of duration, Bonds with high coupon rates and, in turn, high yields will tend to have lower durations than bonds that pay low coupon rates or offer low yields. This makes empirical sense, because when a bond pays a higher coupon rate or has a high yield, the holder of the security receives repayment for the security at a faster rate.

in essence,the issue of yields does affect the term structue otherwise the cbk would not be interested in graphing the yield curve would they?
Scubidu
#9 Posted : Monday, August 16, 2010 1:01:45 PM
Rank: Veteran

Joined: 9/4/2009
Posts: 700
Location: Nairobi
Ya'll need to keep this post going.

@scooby. What’s your take on the rise of some of the yield curves? 91D, 182D and 15 yr yld have risen marginally. Given the liquidity there's no profit incentive in lowering the 91D to interbank right?
“We are the middle children of history man, no purpose or place. We have no great war, no great depression. Our great war is a spiritual war, our great depression is our lives!" – Tyler Durden
Scooby
#10 Posted : Monday, August 16, 2010 5:50:08 PM
Rank: Member

Joined: 9/2/2006
Posts: 121
Hi all,

@emlyn, please clarify this for me. What is the difference between holding a 12.5% interest free KenGen bond with a duration of 10 years and and a 12% CfC Stanbic bond for 7 years?

@scubidu, the rise in the interest rates for 91 days and 182 days was bound to happen anytime from now. Currently, the real interest rates is negative i.e. current rates are not enough to cover for the inflation. This is the same thing that happened in 2003/2004.
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