                                 In the

        United States Court of Appeals
                   For the Seventh Circuit
                       ____________________
No. 15-1180


UNITED STATES OF AMERICA,
                                                     Plaintiff-Appellee,

                                   v.

YIHAO PU,
                                                 Defendant-Appellant.
                       ____________________

           Appeal from the United States District Court for the
             Northern District of Illinois, Eastern Division
             No. 11 CR 00699 — Charles R. Norgle, Judge
                       ____________________

        ARGUED MAY 26, 2015 — DECIDED FEBRUARY 24, 2016
                    ____________________

    Before BAUER, KANNE, and WILLIAMS, Circuit Judges.
    WILLIAMS, Circuit Judge. Yihao Pu worked for two compa-
nies, “Company A 1” and Citadel, which are financial institu-
tions that traded stocks and other assets on behalf of clients.
While working at each company, Pu copied computer files

    1 The parties’ briefs refer to the organization as “Company A,” so we
will do the same.
2                                                         No. 15-1180


from his employer’s system to personal storage devices. The
files were part of each company’s proprietary software that
allowed them to execute strategic trades at high speeds. The
files were company trade secrets, and Pu’s copying of the files
was a significant data breach.
    Normally, crimes involving the theft of computer data
trade secrets lead to the sale of the data to, or the thief being
hired by, a company that will use the data. But here, Pu used
the data to conduct computerized stock market trades for
himself and lost approximately $40,000.
    Pu was indicted and pleaded guilty to one count of unlaw-
ful possession of a trade secret belonging to Company A, and
one count of unlawful transmission of a trade secret belong-
ing to Citadel. The district court sentenced him to 36 months
in prison and ordered him to pay over $750,000 in restitution.
Pu appeals, arguing that the district court’s factual findings
did not support its conclusion that Pu intended to cause a loss
to the companies of approximately $12 million. We agree. Pu
also challenges the district court’s failure to require the gov-
ernment to provide a complete accounting of the loss caused
by his offense before it determined the amount of restitution
owed. We also agree that the district court erred by awarding
restitution without evidence that reflected a complete ac-
counting of the victims’ investigation costs.
                       I. BACKGROUND
   Yihao Pu is a twenty-eight-year-old quantitative finance
(“QF”) professional. 2 Pu worked as a QF analyst at Company


    2 QF professionals apply mathematical concepts and techniques to fi-
nancial markets.
No. 15-1180                                                  3


A from July 2009 to March 2010 and as a QF engineer at Cita-
del from May 2010 to August 2011.
    Company A and Citadel, the victims in this case, are finan-
cial firms that engage in high frequency trading (“HFT”). HFT
is the rapid buying and selling of publicly traded stocks. Both
companies developed proprietary computer programs, which
we will call HFT platforms, that perform the tasks necessary
to execute trades at lightning fast speeds when certain market
events occur. Company A and Citadel’s HFT platforms are
valuable trade secrets. Both companies use their HFT plat-
forms to conduct trades for themselves or their clients. Com-
pany A also developed infrastructure software, which is sold
to customers and allows them to execute their own high fre-
quency trades using Company A’s technology.
    Each company put substantial money and time into creat-
ing its unique HFT platform. For their respective entities,
Company A and Citadel employees developed and imple-
mented HFT strategies by analyzing and utilizing mathemat-
ical and statistical models of investment instruments and
market activities. The HFT strategies identified short-term in-
vestment opportunities in the stock market or other asset mar-
kets. This information was then translated into algorithms.
The algorithms were basically computerized instructions for
when to order a trade. They were incorporated into the com-
puter source code that ran the HFT platforms or Company A’s
infrastructure software. Citadel’s algorithms also generated
outputs that were expressed as numerical values, which Cita-
del called alpha data. The algorithms also contained alpha
terms, which generated numerical values, which Citadel
called alpha term data. Both alpha data and alpha term data
are component parts of Citadel algorithms and not algorithms
4                                                   No. 15-1180


or source code themselves. The numerical value derived from
this application reflects a specific moment in time. Lastly, Cit-
adel’s trade secrets also included program files in the “R” and
“C” programming languages (“R/C files”) that are not algo-
rithms themselves, but are used to test and optimize an algo-
rithm’s effectiveness.
    While working at Company A and then Citadel, Pu ille-
gally copied files that were trade secrets belonging to each
company and transferred the files to personal electronic stor-
age devices. Specifically, he copied Files 1 and 2 from Com-
pany A’s HFT platform and infrastructure source code. Pu
copied Files 3–9 of alpha and alpha term data owned by Cita-
del. Files 3–6 were alpha data owned by Citadel. Files 3–4 also
included alpha term data. Files 7–9 were R/C files owned by
Citadel. Suspicious of the activity on Pu’s work computer,
Citadel questioned Pu and conducted an internal investiga-
tion to figure out the extent of the data breach related to Pu’s
criminal activity.
   The grand jury charged Pu with nine counts of wire fraud,
18 U.S.C. § 1343, four counts of unlawful transmission of
trade secrets, 18 U.S.C. § 1832(a)(2), six counts of unlawful
possession of trade secrets, 18 U.S.C. § 1832(a)(3), three counts
of unauthorized access of a protected computer, 18 U.S.C.
§ 1030(a)(2)(C), and one count of obstruction of justice, 18
U.S.C. § 1519. Pursuant to a written plea agreement, Pu
pleaded guilty to one count of unlawful possession of a trade
secret belonging to Company A and one count of unlawful
transmission of a trade secret belonging to Citadel.
   At sentencing, the district court adopted the Presentence
Investigation Report (“PSR”) and its findings for sentencing
purposes. The parties agreed, and the district court found,
No. 15-1180                                                      5


that there was no actual monetary loss. Pu objected to the
PSR’s loss calculation with respect to the intended loss
amount arguing that there was no intended loss. However,
the district court disagreed. Relying on the government’s cal-
culation and the findings in the PSR, the district court found
that total development costs of the algorithms or source code
was the appropriate metric to value the files Pu stole. From
the evidence, the district court concluded that Files 1 and 2
cost Company A $2,192,250 to develop and Files 3–9 cost Cit-
adel $10,102,647 to develop. Ten million dollars was at-
tributed to Files 3–6 and $102,647 was attributed to Files 7–9.
These figures essentially represent how much money the
companies paid their respective employees to develop the al-
gorithms or source code, excluding overhead. The district
court added these totals and found that the intended loss
amount was $12,294,897.
    In calculating Pu’s advisory guidelines sentence under
U.S.S.G. § 2B1.1 (2014), the district court determined that Pu’s
base offense level was a six. The court imposed a two-level
increase for each of the following: (a) use of a specialized skill,
(b) sophisticated means, and (c) obstruction of justice. This
brought his offense level to 12. As stated above, the district
court found that the government had met its burden to prove
intended loss and held that the combined intended loss to
both victims was approximately $12,000,000. This loss calcu-
lation resulted in an additional twenty-level increase. After
factoring in a two-level decrease for acceptance of responsi-
bility and one-level decrease for a timely guilty plea, the sen-
tencing judge reduced Pu’s offense level to 29. Because he has
a criminal history category I, his guideline-recommended
sentence was 87–108 months.
6                                                     No. 15-1180


    While examining the sentencing factors under 18 U.S.C.
§ 3553, the district court found that although there was evi-
dence that hinted that Pu had a larger scheme to use the stolen
files, the only criminal conduct here that was proven was that
Pu copied the files onto his personal electronic storage device,
and the government had not presented sufficient evidence of
a greater plan than what Pu actually achieved. Noting Pu’s
youth, his family ties, and his lack of prior criminal history,
and balancing this information with the seriousness of the
crime, the district court determined that the guidelines sen-
tence overstated the seriousness of the offense and departed
downward, sentencing Pu to 36 months’ incarceration. The
district court also sentenced Pu to three years of supervised
release.
    The district court found that although there was no actual
loss for guidelines purposes, Citadel incurred an actual loss
for restitution purposes. Citadel spent money on computer fo-
rensic analysts and attorneys during its internal investigation
after the initial discovery of Pu’s criminal activity, which is
recoverable as restitution. Because Citadel also has ongoing
civil litigation against Pu and the lack of detail in the govern-
ment’s letter from Citadel regarding restitution, Pu argued
that Citadel had included in its restitution figure analysts and
attorneys’ fees associated with the civil litigation and objected
to the restitution figure. The district court overruled the ob-
jection, relying on a letter from Citadel that stated that the res-
titution amount requested did “not include the amount that
Citadel paid other outside legal counsel to represent Citadel
No. 15-1180                                                           7


in its civil suit against Pu.” The district court then held Pu li-
able for restitution to Citadel in the amount of $759,649.55. 3
Pu appeals his sentence challenging the loss calculation and
the restitution amount.
                          II. ANALYSIS
   Pu challenges the district court’s intended loss calculation
of $12,000,000, which resulted in a twenty-point enhance-
ment. Pu makes many arguments to support his challenge,
but generally, he contends that the district court’s findings do
not support its loss calculation. We agree.
    We review de novo the district court’s definition of loss, the
method it uses to measure the loss, and the sentencing proce-
dure. United States v. Domnenko, 763 F.3d 768, 775 (7th Cir.
2014). We review the district court’s loss calculation for clear
error. Id. When evaluating the district court’s sentencing pro-
cedure, we look to see if the district court properly calculated
the guidelines range, treated the guidelines as advisory, se-
lected a sentence based on facts that were not clearly errone-
ous, and adequately explained the chosen sentence. See Gall v.
United States, 552 U.S. 38, 51 (2007).
    We have often stated that “[t]he district court must say
enough to ‘satisfy the appellate court that it has considered
the parties’ arguments and has a reasoned basis for exercising
its own legal decisionmaking authority.’” United States v.
Marin-Castano, 688 F.3d 899, 902 (7th Cir. 2012) (quoting Rita
v. United States, 551 U.S. 338, 356 (2007)). The district court

   3    There was a co-defendant in this case, Sahil Uppal, who worked
with Pu at each company. Uppal is not relevant to the appeal, but we
acknowledge that the district court held Pu and Uppal jointly and sever-
ally liable for the restitution amount.
8                                                  No. 15-1180


must address “a defendant’s principal arguments that are ‘not
so weak as to not merit discussion.’” United States v. Howard,
729 F.3d 655, 664 (7th Cir. 2013) (quoting United States v. Cun-
ningham, 429 F.3d 673, 679 (7th Cir. 2005)). This is an im-
portant procedural rule. United States v. Lockwood, 789 F.3d
773, 783 (7th Cir. 2015) (quoting Gall, 552 U.S. at 50).
    A. District Court’s Intended Loss Calculation Was
    Clearly Erroneous.
    At the sentencing hearing, the parties agreed that there
was no actual loss, and the district court entered a finding of
no actual loss. The parties disputed the intended loss amount.
Pu objected to the PSR’s loss calculation, specifically arguing
that the cost to Citadel of developing the source code that pro-
duced the outputs Pu stole should not be imputed wholesale
to the value of the stolen data because the outputs of the
source code are not the same, or as valuable, as the source
code that was developed by Citadel employees. He also ar-
gued that the intended loss amount should be zero, or at most
$2,000, because the government failed to prove that Pu in-
tended to copy the source code or do more than use the out-
puts to conduct personal trades. For both these reasons, Pu
argued, the underlying conduct was not tied to the PSR’s loss
calculation.
   The general rule is that the district court determines the
greater of actual or intended loss. U.S.S.G. § 2B1.1 n.3(A)
(2014). The guidelines define intended loss as “the pecuniary
harm that was intended to result from the offense,” which “in-
cludes intended pecuniary harm that would have been im-
possible or unlikely to occur.” See id. at n.3(A)(ii). Pecuniary
harm is monetary harm or a harm that is readily measurable
in money; it does not include non-economic harm. Id. at
No. 15-1180                                                               9


n.3(A)(iii). “Intended loss analysis, as the name suggests,
turns upon how much loss the defendant actually intended to
impose” on the victim, regardless of whether the loss actually
materialized or was even possible. United States v. Higgins, 270
F.3d 1070, 1075 (7th Cir. 2001); see also United States v. Middle-
brook, 553 F.3d 572, 578 (7th Cir. 2009) (“[T]he true measure of
intended loss [is] in the mind of the defendant.”). 4 The
phrase “result from” imposes a requirement of but-for causa-
tion. See Burrage v. United States, 134 S. Ct. 881, 886–88, 891
(2014) (finding when a statute does not define the phrase “re-
sult from,” the court should give it its ordinary meaning,
which is actual or but-for causation). Finally, if a loss occurred
but the sentencing court cannot reasonably determine the
amount of the loss, it may use the gain that resulted from the
offense as an alternative measure to estimate the loss amount.
See U.S.S.G. § 2B1.1 n.3(B).
   The district court need only make a reasonable estimate of
the loss amount. Id. at n.3(C). As relevant here,
        The estimate of the loss shall be based on available infor-
        mation, taking into account, as appropriate and practica-
        ble under the circumstances, factors such as the follow-
        ing:
        (i) The fair market value of the property unlawfully taken,
        copied, or destroyed; or, if the fair market value is imprac-
        ticable to determine or inadequately measures the harm,
        the cost to the victim of replacing that property.




    4  The current version of the guidelines seems to incorporate this prin-
ciple into the notes, defining intended loss as “the pecuniary harm that the
defendant purposely sought to inflict.” See U.S.S.G. § 2B1.1 n.3(A)(ii)
(2015).
10                                                          No. 15-1180


       (ii) In the case of proprietary information (e.g., trade se-
       crets), the cost of developing that information or the re-
       duction in the value of that information that resulted from
       the offense.

Id. at n.3(C)(i)–(ii). And “[t]he government must show the loss
amount caused by the conduct of conviction and other rele-
vant unlawful conduct by a preponderance of the evidence.”
United States v. Khan, 771 F.3d 367, 379–80 (7th Cir. 2014).
    The probation officer explained the PSR’s intended loss
calculation relied on the guidelines statement that the sen-
tencing judge may estimate the loss amount by considering
“[i]n the case of proprietary information (e.g., trade secrets),
the cost of developing that information or the reduction in the
value of that information that resulted from the offense.”
U.S.S.G. § 2B.1. n.3(C)(ii); see also Sent’g Hr’g Tr. 31. She fur-
ther explained that “the total amount of loss is based on the
figure that was provided by Citadel, that their cost for re-
search and development to build that information that was
stolen was approximately the 10.1 million, and that [Com-
pany A] … provided a figure of approximately 2.6.” Sent’g
Hr’g Tr. 31.
   The government explained the $12 million slightly differ-
ently, labeling its calculation as “intended loss” but seemingly
describing Pu’s gain, stating:
       [T]he intended loss is calculated in terms of the amount
       of work and effort that went into creating the trade se-
       crets. That’s where this $12 million figure comes from. …
       Citadel didn’t lose the value of its employees’ salaries or
       wages or costs. It just goes into the Court’s determination
       of whether he was intending to obtain this product from
       Citadel unlawfully, and the costs that basically he
       avoided by stealing these things rather than creating
       them on his own.
No. 15-1180                                                          11


Id. at 19–20.
   In making the loss determination, the district court found
that:
       [T]he government‘s version [of the loss amount] states
       that the intended loss that should be applied to Defend-
       ant Pu’s participation in the instan[t] offense is approxi-
       mately $12,745,796. This includes approximately
       $10,102,647 in research and development costs Citadel
       spent; approximately $2,643,149 [Company A] spent; for
       the trade secrets Defendant Pu stole from both compa-
       nies.
       It is Defendant Pu’s position that the loss attributable to
       his participation in the instant offense is zero?
       And I have already said that the Court would adopt the
       findings of the probation department, and cited numer-
       ous cases to support that position. And a defendant who
       wishes to challenge a factual finding in the PSR must do
       so with evidence, and not with simple denials.
       I think there is enough certainly from the government’s
       standpoint—and as established by the probation officer’s
       determination—that the loss here, foreseeable loss is $12
       million.

Id. at 31–32.
    Later, when looking at the 18 U.S.C. § 3553 factors the dis-
trict court stated that:
       The evidence is not quite clear on whether you might
       have gone beyond what you did in this case had you not
       been interrupted; had your employers and others not dis-
       covered what you had been doing. One view might be
       that this was embryonic and there was more to come. But
       there is no solid evidence to indicate that you would have
       used these secrets to try to help yourself to improve your
       financial situation. There is no evidence before the Court
       to suggest that there was some grander scheme or some
12                                                            No. 15-1180


         grand plan or design to what you were doing. There are
         suggestions or hints of it, but not enough for the Court to
         say that this was just the beginning of a greater endeavor
         on your part. And so it appears that it did begin and end
         with what you did in the case.

Id. at 79–80.
    We do not doubt that the cost of development of the trade
secrets was an easy figure to use when making the intended
loss calculation. The guidelines suggest that the cost of devel-
opment is the metric to use to estimate loss in a trade secrets
case. See U.S.S.G. § 2B1.1 n.3(C)(ii). But the real question is
whether the government proved by a preponderance of the
evidence that the cost of development of the trade secrets was
the correct loss figure. See United States v. Berheide, 421 F.3d
538, 541 (7th Cir. 2005). To answer this, we must determine
whether the record supports a finding that it was more likely
than not that Pu intended to cause a loss to the victims that
equaled the cost of development. See id. We conclude that it
does not. There is no direct evidence of how much of a loss Pu
intended Company A and Citadel to suffer. There is also no
evidence from which we can infer how much of a loss Pu in-
tended the victims to suffer. The evidence shows that the cost
of development was $12 million. 5 By finding a $12 million in-
tended loss amount, the district court determined that the

     5 It is arguable whether the figure for the cost of development of Cit-
adel Files 3–6 was correct since these files were only component parts of
an algorithm. The government presented evidence of the cost of develop-
ment for the algorithms that generated the component parts, Files 3–6, that
Pu stole. Is the cost of development of the algorithms that generated the
component parts stolen the same as the cost of development of the com-
ponent parts only? The record does not answer this question. And the dis-
trict court did not address Pu’s argument that raised this concern. See infra
§ II.B. Since we do not need to answer it to determine whether there was
No. 15-1180                                                               13


government proved by a preponderance of the evidence that
Pu intended to cause the victims to suffer a $12 million loss.
However, evidence of Pu’s intent to cause the victims any loss
is not in the record. Because the record does not support the
district court’s conclusion, we find it to be clearly erroneous.
   The record does not provide enough information for us to
determine what the correct intended loss amount is.
    It seems that the probation officer and the district court
simply looked at the evidence and determined that an in-
tended loss amount was required because there was no actual
loss. Then, because the guidelines state that the court may es-
timate loss in a trade secrets case by considering the value of
the trade secrets, they simply stated the trade secrets’ pur-
ported value was the intended loss amount without any anal-
ysis about whether that metric worked with the circum-
stances of Pu’s case. The guidelines state that in a trade secrets
case, the cost of developing the information should be a factor
taken into account to estimate the loss amount when the fac-
tor is “appropriate and practicable under the circumstances.”
U.S.S.G. § 2B1.1 n.3(C). Without evidence of Pu’s intent to
cause the victims to suffer a loss equal to the cost of develop-
ment, the district court’s use of the cost of development to de-
termine the intended loss amount was not appropriate.
   Moreover, as a practical matter, the district court’s in-
tended loss calculation conflicts with its finding that there
was insufficient evidence of a grander scheme that was inter-
rupted. Intended loss is often used to capture the loss the vic-
tim would or could have suffered had the offender been able


an error, we assume, for purposes of this appeal, that the $12 million figure
accurately represented the cost of development.
14                                                    No. 15-1180


to complete his interrupted criminal scheme. Here, the district
court found that the government did not prove that Pu was
interrupted before completing a criminal act. His conduct was
merely what was charged. The district court did not explain
how Pu intended to cause a $12 million loss through his con-
duct, whether by considering charged conduct or relevant
conduct. Usually, we can clearly see how the loss would have
come about. For example, say, a defendant stole a credit card
with a $20,000 limit. There was evidence that he intended to
make enough purchases with the credit card to reach the
credit limit, but he was caught and charged with stealing the
credit card before he had the opportunity to use it. Cf. United
States v. Mei, 315 F.3d 788, 791–93 (7th Cir. 2003). Like Pu’s
case, there would be no actual loss to the owner of the credit
card. Unlike Pu’s case, however, we could clearly see that an
intended loss amount of $20,000 would be proper because
there was evidence that he intended to purchase items until
he reached the credit limit of the credit card. Here, the district
court’s only finding regarding Pu’s intent further suggests
that the intended loss finding was erroneous.
    “Where a district court selects a guidelines range by rely-
ing on a clearly erroneous factual finding, ‘we are obliged to
remand for resentencing unless, reviewing the record as a
whole, we can conclude that the error was harmless, i.e., that
the error did not affect the district court’s selection of the sen-
tence imposed.’” United States v. McMath, 559 F.3d 657, 670
(7th Cir. 2009) (quoting United States v. Hollis, 230 F.3d 955,
958 (7th Cir. 2000)). It appears that the erroneous loss calcula-
tion affected the sentence. Without a correct intended loss
finding there is no basis for the twenty-point offense level in-
crease. Although the district court departed downward, it
may have sentenced Pu differently had it been departing from
No. 15-1180                                                      15


a different guideline range. We must vacate and remand for
resentencing. See Berheide, 421 F.3d at 541–42 (holding that the
district court’s erroneous factual finding as to the intended
loss amount justified a remand).
   B. District Court Erred by Failing to Address Pu’s Argu-
   ments.
    As stated above, Pu disputed the loss calculation, specifi-
cally arguing that the cost to Citadel of developing the source
code should not be used because Pu only stole the outputs the
source code generated, not the actual source code. Neither the
PSR nor the record of the sentencing hearing addressed this
argument. The full value of the development of the source
code was attributed to Pu’s theft without comment. Pu also
argued that because the government presented no evidence
that he intended to do more than he actually did with the sto-
len outputs, which both sides agreed generated no actual loss,
the intended loss should be zero, or at most $2,000. We find
that Pu’s arguments were not frivolous.
    A district court’s failure to explain the rejection of a non-
frivolous argument requires resentencing. United States v.
Martin, 718 F.3d 684, 687 (7th Cir. 2013); see also United States
v. Villegas-Miranda, 579 F.3d 798, 801 (7th Cir. 2009) (“The
court must state its reasons for rejecting a defendant’s princi-
pal arguments if the arguments have merit.”). In the loss cal-
culation, neither the PSR nor the district court addressed or
analyzed these arguments. By not addressing these argu-
ments, the district court erred. See Martin, 718 F.3d at 687–88;
see also Rita v. United States, 551 U.S. at 356–57 (finding that the
district court “should set forth enough [of an explanation] to
satisfy the appellate court that he has considered the parties’
arguments”). This is true even though the district court gave
16                                                   No. 15-1180


detailed reasons for the sentence it imposed. See Villegas-Mi-
randa, 579 F.3d at 802. The error is not harmless “because we
can never be sure of what effect it had, or could have had, on
the court’s decision.” Id.
    Additionally, in adopting the PSR, the district court ad-
monished the defense that a challenge to a factual finding
must be done with evidence and not “simple denials.” Pu had
challenged the factual findings with more than denials. He
submitted a written report of an expert on his behalf. Alt-
hough the district court later acknowledged, during argu-
ments concerning § 3553(a) factors, that the defendant had
supported his position with written submissions, it did not
address or engage in any analysis of these materials. From the
record of the sentencing hearing, the district court appears to
have taken no consideration of the defendant’s expert materi-
als in making its loss calculation or determining Pu’s sen-
tence. The evidence may have had, at least, some effect on the
intended loss calculation. See United States v. Schneider, 930
F.2d 555, 559 (7th Cir. 1991). Again, because of the district
court’s silence on the issue, we cannot be sure of the effect that
the evidence had, or could have had, on Pu’s sentence. See
Leiskunas, 656 F.3d at 738. On remand the district court should
address Pu’s arguments and evidence when calculating the
intended loss amount.
     C. Finding of Economic Loss Not Required.
    For the sake of completeness, we will address the mistake
of law Pu alleges. Pu argues that the district court erroneously
believed that it was required to find an economic loss because
Pu was convicted. It is unclear what the district court be-
lieved, but our impression from the record is that the district
No. 15-1180                                                    17


court may have thought that Pu’s conviction mandated a find-
ing of an economic loss to the victims of an amount that was
greater than zero. No such finding was required.
    Pu argued at sentencing that the proper loss calculation in
this case was zero because he did not intend to cause financial
harm to either of the victims of his theft. When Pu’s counsel
made this argument, the district court asked whether this
meant that the case should not have come to court, suggesting
that it thought that it must find some loss amount for a crime
to exist. The statute of conviction, 18 U.S.C. § 1832, does not
explicitly require an economic loss to the victim. See 18 U.S.C.
§ 1832(a)(2)–(3) (“Whoever, with intent to convert a trade se-
cret … to the economic benefit of anyone other than the owner
thereof” copies or possesses a trade secret shall be fined or
imprisoned.); see also United States v. Hanjuan Jin, 733 F.3d 718,
721–22 (7th Cir. 2013) (finding that the “government does not
have to prove that the owner of the trade secret actually lost
money” because of the theft and noting that although the sto-
len trade secrets may have economic value, it may be impos-
sible to monetize the value, or the injury may be the uncover-
ing of the fact that a company cannot protect its trade secrets).
Further, Pu’s plea agreement admits that he intended to con-
vert a trade secret for economic benefit to someone other than
the owner, not that he intended to cause an economic loss to
the victims.
    Additionally, the guidelines do not require a loss calcula-
tion greater than zero. See Schneider, 930 F.2d at 559. The loss
determination is a special offense characteristic that increases
the guidelines offense level. The loss amount leads to “bonus
punishment points,” which express a reasonable estimation
of the victim’s financial loss. Id.; see U.S.S.G. § 2B1.1(b) &
18                                                   No. 15-1180


n.3(A),(C); see also United State v. Lopez, 222 F.3d 428, 437 (7th
Cir. 2000) (“Additional punishment is merited where suffi-
cient evidence provides for determination of monetary
loss.”). If there was a loss, but it cannot reasonably be deter-
mined, the district court could look at Pu’s gain. U.S.S.G. §
2B1.1, n.3(B).
    “A mistake of law generally satisfies clear error, de novo,”
or abuse of discretion review. McMath, 559 F.3d at 663 n.2. If
the district court misunderstood the law, it would have com-
mitted an error requiring remand. However, because we re-
verse on other grounds, we need not decide whether the dis-
trict court misunderstood the law. We include this analysis to
aid the district court on remand.
     D. District Court Erred Deciding Restitution Amount.
    Pu contends that the district court erred by failing to re-
quire the government to provide a complete accounting of the
victim’s losses and authorizing a restitution amount that was
unreasonable, lacked evidentiary support, and included pro-
hibited expenses incurred by Citadel in connection to its civil
lawsuit against Pu. Although Pu challenged the restitution
amount below, he only argued that the restitution amount
was improper because the government’s evidence lacked
specificity and included expenses from Citadel’s civil case.
The government argues that Pu “twice affirmatively repre-
sented during the sentencing hearing that [he] had no objec-
tion to restitution for expenses incurred during Citadel’s in-
ternal investigation.” But the two statements the government
relies on do not establish a waiver of these issues. Defense
counsel stated that the measure of restitution should be Cita-
del’s costs related to its internal investigation and that he
“would not object to [costs] that had to do with [its] internal
No. 15-1180                                                      19


investigation if the costs were reasonable.” These assertions
concede that restitution is due for Citadel’s internal investiga-
tion costs. They do not affirmatively state that Pu had no ob-
jection to the expenses occurred during the investigation. We
find no waiver. However, because Pu did not make the rea-
sonableness and sufficiency of the evidence arguments at the
time of sentencing, we will review those issues for plain error.
See, e.g., United States v. Walker, 746 F.3d 300, 308 (7th Cir.
2015).
    Because Pu argued below that the restitution amount in-
cluded prohibited expenses, we review that issue for abuse of
discretion. See United States v. Hosking, 567 F.3d 329, 331 (7th
Cir. 2009). In this context, we view the evidence in the light
most favorable to the government. Id. “We will disturb a res-
titution order only if the district court relied upon inappropri-
ate factors when it exercised its discretion or failed to use any
discretion at all.” United States v. Havens, 424 F.3d 535, 538 (7th
Cir. 2005). When “the record does not sufficiently support [the
district court’s] conclusions or clarify its reasoning, then we
ask that the court provides us with that information, includ-
ing its specific findings of fact, to facilitate our review.” United
States v. Menza, 137 F.3d 533, 538 (7th Cir. 1998). A restitution
award may include costs incurred by a corporate victim in
conducting an internal investigation of the offense. Hosking,
567 F.3d at 332. This may include attorney fees or fees paid to
other professionals hired to participate in the investigation.
See id.
   The government entered into evidence a letter signed by
Shawn Fagan, senior deputy general counsel at Citadel,
which stated that Citadel sought $759,649.55 in restitution.
The letter also stated that the amount reflects what Citadel
20                                                          No. 15-1180


spent on computer forensic analysts and the outside legal
counsel that it hired to conduct an internal investigation after
it discovered Pu had copied data:
       Specifically, Citadel paid legal counsel $151,500.50 to con-
       duct its internal investigation … . This amount reflects
       323.7 hours of work, billed by nine lawyers, paralegals,
       and legal assistants with hourly billing rates ranging from
       $115.50 to $630. During this period, Citadel paid FTI
       $608,149.05 for 1818.8 hours of work billed by sixteen an-
       alysts with hourly billing rates ranging from $171 to $567.

The letter also indicated that the amount did not “include the
amount that Citadel paid other outside legal counsel to repre-
sent Citadel in its civil suit against Pu” or expenses. On this
evidence, the district court essentially found that the costs
were not related to the civil case. The district court was within
its discretion in making this finding because the record sup-
ports it. Nonetheless, the restitution determination suffers
from an error.
    “The district court is required to base its restitution order,
to the extent practicable, on a ‘complete accounting’ of the
loss.” Hosking, 567 F.3d at 332. Defendant argues that the res-
titution amount is unreasonable and lacks evidentiary sup-
port because the Fagan letter fails to give a complete account-
ing of the losses. We agree.
    In Hosking, the government sought restitution to reim-
burse a bank for expenses for its internal investigation. To
support its request for restitution, the government submitted
a single document that listed the name and title of each bank
employee who worked on the investigation, the employee’s
hourly wage, and the number of hours spent on the investi-
gation. The document included a brief description of the
scope of the investigation and what a few employees did, but
No. 15-1180                                                   21


generally failed to describe the work done by each employee.
The district court reviewed the evidence and cut the re-
quested amount in half, finding restitution proper and that
the reduced amount was “clearly legitimate.” Id. at 331–33.
We vacated and remanded the restitution order because we
found that the district court entered the order without ex-
plaining why it relied on the document and without requiring
evidence that the costs reported were directly and reasonably
caused by Hosking’s fraud. The lack of detail left us unable to
discern whether the costs incurred by each employee’s work
on the investigation were appropriate and reasonable. On re-
mand, we required the government to submit evidence and
an explanation of how each employee’s time was spent on the
investigation. We further stated that “there must be an ade-
quate indication that the hours claimed are reasonable” and
that the costs were incurred in investigation of the fraud. Id.
at 344.
    Citadel’s restitution letter suffers from many of the same
deficiencies as the Hosking restitution evidence. As a result,
the district court erred by awarding restitution without evi-
dence that reflected a complete accounting of the investiga-
tion costs. The letter does not explain how any attorney’s time
was spent on the investigation, and there is no information
that provides an adequate indication that the hours were rea-
sonable. Even the Hosking restitution evidence provided some
description of what employees did to investigate the fraud.
Here, we do not know what work the attorneys did. The dis-
trict court concluded that the amount included divers that
were hired to retrieve hard drives from a canal and money
spent cooperating with the Federal Bureau of Investigation.
Did the attorneys do these activities, or was it the forensic an-
alysts? There is simply not enough information in the record
22                                                    No. 15-1180


for us to meaningfully review the restitution order. As to the
forensic analysts, the record reveals that they analyzed data
to determine what data was taken and where that data was
stored. That information is helpful, but it does not help us
evaluate whether the cost incurred for over 1,800 hours of
work in a one-month period was reasonable. A letter like the
one submitted coupled with invoices from the firms would be
more helpful. This was a tough case. The district court had
complex issues to work through in order to sentence Pu. As
in Hosking, the government must provide an explanation,
supported by evidence, of how each professional’s time was
spent investigating the data breach, being certain that the ev-
idence provides “adequate indication that the hours claimed
are reasonable.” Id. at 334. Then, the court must ensure that
the amount claimed was in fact incurred by the investigation
of Pu’s misconduct. Id.
   In light of Hosking, we find the district court’s error plain.
We are only required to correct such error if it affects Pu’s
substantial rights. United States v. Kieffer, 794 F.3d 850, 854 (7th
Cir. 2015). By awarding a restitution amount without a com-
plete accounting, the district court may have required Pu to
pay more restitution than he owed. This error affects Pu’s sub-
stantial rights. See United States v. Allen, 529 F.3d 390, 397 (7th
Cir. 2008). So, we vacate the restitution order.
                      III. CONCLUSION
    For the reasons stated, we VACATE Pu’s sentence and the
restitution order and REMAND for resentencing.
