I don’t know how to post images but this is from the Duke case in the online practice problems. What does the below mean?
A long position in backwardation will produce a greater roll return than a position in contango if the price increases. In backwardation, futures prices with a longer time to maturity are lower than the current spot price. In contango, the futures price is greater than the spot price.
Spot (Mar 14) - 945 May 14 - 932 Jul 14 - 887 Sep 14 - 872 Dec 14 - 871 Mar 15 - 858
How do I calculate the roll return? The question states a 5% increase in price in the next 12 months.
Compared to exhibit 16 from page 49 where the futures prices are increasing, the futures prices shown in this problem are decreasing. Yet, both are considered backwardation???
When In backwardation you tend to gain, as you will be buying a lower price future, and as the prices converge o the future spot you tend to gain. Here the 5% return will increase the exoected spot price at the time of closing out your long future. This increases your return even more as the contarct was already in contango.
Eg In here the returns that will be gained hypothetically if the future were to converge to the expected spot it would be as:
Future bought at 858 eaving with a absolute return of 120.6 or % return of 14.06%
Your interpretation can simply also be that the 5% is from the price where you have bought and since it is a long position that will yield you a gain of 5%
I suppose that they assume that, due to the fact that in the LT, E® from holding commo investments is assumed equal to zero and given that margin are invested in RFR => in the LT, index funds will earn 0+RFR=RFR, on average.
When In backwardation you tend to gain, as you will be buying a lower price future, and as the prices converge o the future spot you tend to gain. Here the 5% return will increase the exoected spot price at the time of closing out your long future. This increases your return even more as the contarct was already in contango.
Eg In here the returns that will be gained hypothetically if the future were to converge to the expected spot it would be as:
Future bought at 858 eaving with a absolute return of 120.6 or % return of 14.06%
Your interpretation can simply also be that the 5% is from the price where you have bought and since it is a long position that will yield you a gain of 5%
Either ways you will gain"
I agree on the final results but not on calculations. IMHO, E(sell price on march 15) = Spot(march14)*1.05 = 992.25. RR = 992.25/858-1=15.65% (for Wheat) - 9.23% (for AUD) - (-1.31% for Crude oil).
Backwardation => You buy F F is expected to converge to future S. In this case, future Spot increase by 5%. Eventually, you buy F and you sell at S+5%. Case of wheat and AUD.
Cantango => reverse. Case of crude oil.
So final answer is the same but not the calculations.
"Based on Exhibits 2 and 3, assuming a 5% increase in prices for each underlying asset in the next 12 months, DPAM will most likely obtain the largest roll return from: "
I think bbrv and nishit are wrong - you guys are double counting - roll return is simply the return from rolling; when u add spot return and collateral yield; it results in final yield
however return just between futures also has spot return in it; for ex see q31 cfai
1)long wheat - market in backwardation -> +ve roll yield given by futures return minus spot return
Futures + spot return = (945-858)/ 945 (assuming you had a dec future in march which=spot price due to convergence) = 9.02% ***spot is included due to supply dynamics***
now imo this plus collateral yield should give u full return on the commodity index.
however the roll return in this case= 9.02-5% (spot return) = 4.02%
if you compute for SHORT AUD position IN BACKWARDATION, your roll return from a simple buy and hold should be -9.32%
similarly for LONG CRUDE in CONTANGO you have -11.4%
