@Cab828 compound frequency is beside the point. Convexity is a simpler calculation under continuous. As modified and Mac convexity converge under continuous, for illustration purposes you get a convexity that is invariant to yield. But thanks for your, er, help and constructive tone
duration = -1/P*slope. The slope is "dollar duration" or the price change estimated by a one unit change in yield, where one unit = 100% = 100*100 basis points = 10,000 basis points! So, it's an incredibly unrealistic estimate of the linear (approximation) changed but useful to duration hedge the portfolio. Thanks,
I am getting a very different answer between the actual changes in bond price for some reason? Not sure why. Is duration a % term rather than the price change in $
Here we have done valuation assuming yield is continously compounded. However while calculating Duration same yield is considered as Annual compounding. Please rectify error
Hi David, in your opinion what are some of the options in pricing an illquid bond? Say i had to mark mtm. Can we take the spread on the cds? It was suggested that we look at a treasury bond and then take a spread...but how would we know what spread to take? Thx
Thanks for sharing! May I ask a question about how you show the duration line on the graph? I can't tell what is the formula for the duration plot when it is changing. Could you please teach me?
Hi! It's looking to the difference between defined yield and % change to the yield set in green area. Due to the fact, that duration and actual are showed here as negative value, the math equation should looks like below: Bond price at duration plot [$] in cell C12 = abs(actual) + [abs(actual) x abs(duration)] x (C5 - B12)
What actualy is your "Actual" value? The video shows formula: =face*EXP(-(C5+1)*T)-face*EXP(-C5*T) Which I understand as: (Price for 104% yield) - (Price for 4% yield), not as the price percentage change. Also "Modified Duration" = "Macaulay Duration" / (1 + yield) which should give positive 28.85. Why do you need this to be negative?
+Stefania Cancellaro Because one 1% change in yield equals "Duration"% change in price, we can write equation like this: x+0.01*x=P+P*D. In this example 2% change (from 4% to 6%) equals 30.12+30.12*28.85*0.02. Hope this'll help.
WTF do they call it duration? Duration gives the impression that it infers time. Second, bonds are contracts between the issuer and the bond holder. Why does it matter what happens to interest rates after the initial transaction if the bondholder intends to hold on to the bond?
1- It's called duration because it measures how long your bond is exposed to fluctuations in interest rates in terms of years. 2- It matters what happens to the rates because they affect the price of your bond. If they go up then the discounting is more powerful and reduces the present value of the future cashflows and vice versa (Bigger denominator).
Hey Jimmy, thanks for the reply. you missed my second point. My assumption was that people hold on to the bond until it matures. Rates are irrelevant if you do not sell the bond. I get that not everyone holds on to the bond until expiration. I realize this now.
Ah yes but they are still relevant. Especially in the case of non-zero coupon bonds. The rates determine the present value of all those coupon/cash flows coming in, in addition to that face value maturity at the end.
@Cab828 compound frequency is beside the point. Convexity is a simpler calculation under continuous. As modified and Mac convexity converge under continuous, for illustration purposes you get a convexity that is invariant to yield. But thanks for your, er, help and constructive tone
duration = -1/P*slope. The slope is "dollar duration" or the price change estimated by a one unit change in yield, where one unit = 100% = 100*100 basis points = 10,000 basis points! So, it's an incredibly unrealistic estimate of the linear (approximation) changed but useful to duration hedge the portfolio. Thanks,
I am getting a very different answer between the actual changes in bond price for some reason? Not sure why. Is duration a % term rather than the price change in $
Here we have done valuation assuming yield is continously compounded. However while calculating Duration same yield is considered as Annual compounding. Please rectify error
Hi David, in your opinion what are some of the options in pricing an illquid bond? Say i had to mark mtm. Can we take the spread on the cds? It was suggested that we look at a treasury bond and then take a spread...but how would we know what spread to take? Thx
Thanks for sharing! May I ask a question about how you show the duration line on the graph? I can't tell what is the formula for the duration plot when it is changing. Could you please teach me?
David, how can I calculate the data in the duration plot highlighted in green. Thanks
Hi! It's looking to the difference between defined yield and % change to the yield set in green area. Due to the fact, that duration and actual are showed here as negative value, the math equation should looks like below:
Bond price at duration plot [$] in cell C12 = abs(actual) + [abs(actual) x abs(duration)] x (C5 - B12)
Hi, Can you provide link to download this excel sheet ?
What is the formula for cells C11, C12 and C13?
please what is the answer to this question?
What actualy is your "Actual" value?
The video shows formula:
=face*EXP(-(C5+1)*T)-face*EXP(-C5*T)
Which I understand as: (Price for 104% yield) - (Price for 4% yield), not as the price percentage change.
Also "Modified Duration" = "Macaulay Duration" / (1 + yield)
which should give positive 28.85. Why do you need this to be negative?
Very nice informative video. Where i could get/learn more about how to build financial models in excel. The formulas, graphs, ect... thx
10 years ago!!!!
Hey , how did you get the graph?
+Stefania Cancellaro Because one 1% change in yield equals "Duration"% change in price, we can write equation like this: x+0.01*x=P+P*D.
In this example 2% change (from 4% to 6%) equals 30.12+30.12*28.85*0.02. Hope this'll help.
WTF do they call it duration? Duration gives the impression that it infers time. Second, bonds are contracts between the issuer and the bond holder. Why does it matter what happens to interest rates after the initial transaction if the bondholder intends to hold on to the bond?
1- It's called duration because it measures how long your bond is exposed to fluctuations in interest rates in terms of years. 2- It matters what happens to the rates because they affect the price of your bond. If they go up then the discounting is more powerful and reduces the present value of the future cashflows and vice versa (Bigger denominator).
Hey Jimmy, thanks for the reply. you missed my second point. My assumption was that people hold on to the bond until it matures. Rates are irrelevant if you do not sell the bond. I get that not everyone holds on to the bond until expiration. I realize this now.
Ah yes but they are still relevant. Especially in the case of non-zero coupon bonds. The rates determine the present value of all those coupon/cash flows coming in, in addition to that face value maturity at the end.
Winston - Financial Models Using Simulation & Optimization (I & II)
merci
thank you
Zero-explanation video