jeffyscott wrote: ↑Sun Aug 14, 2022 8:38 am
#Cruncher wrote: ↑Sun Aug 14, 2022 7:38 am
The right-hand column below shows my calculated YTM for this TIPS for each workday from August 12 to September 30 assuming it is priced to keep the nominal 3.2% return and 122.5646 nominal value at maturity calculated in cell B8. ...
So if someone is looking at this TIPS tomorrow and the reported real YTM is 0.39%, should they be thinking as if they are actually buying at a real YTM of about 0.54%, since that is what we know the real yield would become as of Sept. 30, if
nothing else that would influence TIPS yields/prices were to change over that time period? (underline added)
No, there is nothing special about the yield on 9/30. The YTM on 8/15 is what it is. The table in my post you reference is simply showing that, if the nominal return and the projected nominal redemption value remain the same, the real YTM will change over the period. Note that I'm
not saying "nothing else" changes. On the contrary, it is the
change in the index ratios that causes the effect I'm illustrating.
Kevin M wrote: ↑Sun Aug 14, 2022 4:57 pmThe issue I have is that it's not intuitive to me that a higher real yield could result in a lower nominal return. How would you explain this to someone without crunching the numbers?
I'm afraid I can't explain it without crunching
some numbers, Kevin.
But let's try a fairly simple example: Assume that the Jan 15 2023 TIPS your post references has yields-to-maturity (YTM) of
-0.74% and
-0.66% on 8/8 and 8/9 settlement dates respectively. So the YTM increases 0.08% points in one day. The unadjusted prices can be computed from the yields. And then the total costs (aka adjusted prices) of the purchases these dates (assuming a 0% coupon) will equal the unadjusted price X the index ratio on each day.
Code: Select all
Row Col A Col B Col C Col D Formula in Col B => Col C
2 Matures 1/15/2023
3 Settles 8/08/2022 8/09/2022
4 Days to maturity 160 159 =$B2-B3
5 YTM -0.74% -0.66% Change
6 Unadusted price 100.3261 100.2889 -0.037% =100/(1+B5)^(B4/365)
7 Index ratio 1.27025 1.27082 +0.045%
8 Adjusted price 127.4393 127.4491 +0.008% =B6*B7
Row 8 shows that the total cost increased slightly even though the YTM rose. If the expected nominal proceeds at maturity remain the same, the nominal return must therefore be lower. Column D shows this happens because the increase in the index ratio exceeds the decrease in the unadjusted price.
#Cruncher wrote: ↑Sun Aug 14, 2022 7:38 am... increasing index ratios during August will have a significant effect on the yield of this TIPS even though it doesn't mature until April 15, 2025. (
The effect will be greater for TIPS that mature sooner.) (underline added)
To show this, I modified the table in the
previous post to show the TIPS maturing Jan 15 2023 discussed above. The effect is indeed greater. Instead of the YTM increasing from +0.35% on 8/12 to +0.63% on 9/1 for the April 2025 maturity, it now increases from
-0.42% to +1.50%!
Code: Select all
1 Settles 8/08/2022
2 Matures 1/15/2023
3 Yield to maturity (0.74%)
4 Unadjusted price 100.3261 =100/(1+B3)^((B2-B1)/365)
5 Idx ratio settlement 1.27025 =VLOOKUP(B1,$A$11:$C$46,3,FALSE)
6 Adjusted price 127.4393 =B4*B5
7 Nominal return 2.70%
8 Nominal mature value 128.9363 =B6*(1+B7)^((B2-B1)/365)
Row Col A Col B Col C Col D Col E
9 Adjusted Index Unadj
10 Settles Price Ratio Price YTM
Code: Select all
29 Mon 8/08/22 127.4393 1.27025 100.3261 (0.74%)
30 Tue 8/09/22 127.4486 1.27082 100.2884 (0.66%)
31 Wed 8/10/22 127.4579 1.27138 100.2516 (0.58%)
32 Thu 8/11/22 127.4672 1.27194 100.2148 (0.50%)
33 Fri 8/12/22 127.4765 1.27250 100.1780 (0.42%) <===
34 Mon 8/15/22 127.5044 1.27418 100.0678 (0.16%)
35 Tue 8/16/22 127.5137 1.27474 100.0311 (0.07%)
36 Wed 8/17/22 127.5230 1.27530 99.9945 0.01%
37 Thu 8/18/22 127.5323 1.27587 99.9571 0.10%
38 Fri 8/19/22 127.5416 1.27643 99.9206 0.19%
39 Mon 8/22/22 127.5695 1.27811 99.8111 0.47%
40 Tue 8/23/22 127.5789 1.27867 99.7747 0.57%
41 Wed 8/24/22 127.5882 1.27923 99.7383 0.67%
42 Thu 8/25/22 127.5975 1.27979 99.7019 0.76%
43 Fri 8/26/22 127.6068 1.28035 99.6656 0.86%
44 Mon 8/29/22 127.6347 1.28204 99.5560 1.18%
45 Tue 8/30/22 127.6441 1.28260 99.5198 1.28%
46 Wed 8/31/22 127.6534 1.28316 99.4836 1.39%
47 Thu 9/01/22 127.6627 1.28372 99.4475 1.50% <===
48 Fri 9/02/22 127.6720 1.28372 99.4547 1.49%
49 Mon 9/05/22 127.7000 1.28370 99.4781 1.46%
50 Tue 9/06/22 127.7093 1.28370 99.4853 1.45%
51 Wed 9/07/22 127.7186 1.28369 99.4934 1.44%
52 Thu 9/08/22 127.7279 1.28369 99.5006 1.43%
53 Fri 9/09/22 127.7373 1.28368 99.5087 1.41%
54 Mon 9/12/22 127.7652 1.28367 99.5312 1.38%
55 Tue 9/13/22 127.7746 1.28366 99.5393 1.37%
56 Wed 9/14/22 127.7839 1.28365 99.5473 1.36%
57 Thu 9/15/22 127.7932 1.28365 99.5546 1.34%
58 Fri 9/16/22 127.8025 1.28364 99.5626 1.33%
59 Mon 9/19/22 127.8305 1.28363 99.5852 1.29%
60 Tue 9/20/22 127.8399 1.28362 99.5932 1.28%
61 Wed 9/21/22 127.8492 1.28362 99.6005 1.27%
62 Thu 9/22/22 127.8585 1.28361 99.6086 1.25%
63 Fri 9/23/22 127.8679 1.28361 99.6158 1.24%
64 Mon 9/26/22 127.8959 1.28359 99.6392 1.20%
65 Tue 9/27/22 127.9052 1.28359 99.6465 1.18%
66 Wed 9/28/22 127.9145 1.28358 99.6545 1.17%
67 Thu 9/29/22 127.9239 1.28358 99.6618 1.15%
68 Fri 9/30/22 127.9332 1.28357 99.6698 1.13%
(Index ratios are copied from
this web page.)