FRM EXAM REVIEW COVERS ALL TOPICS PART II FORMULA SHEETS

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1 2016 FRM EXAM REVIEW COVERS ALL TOPICS IN PART II FRM PART II FORMULA SHEETS

3 Cover image: Loewy Design Cover design: Loewy Design Copyright 2016 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) , fax (978) , or on the Web at Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) , fax (201) , or online at Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) , outside the United States at (317) or fax (317) Wiley publishes in a variety of print and electronic formats and by print-on-demand. Some material included with standard print versions of this book may not be included in e-books or in print-on-demand. If this book refers to media such as a CD or DVD that is not included in the version you purchased, you may download this material at For more information about Wiley products, visit Library of Congress Cataloging-in-Publication Data: ISBN

4 Market Risk Management and Measurement (MR)

5 Dowd, Chapter 3 Dowd, Chapter 3 VaR = µ + σz α VaR = ( µ + σz α ) P t 1 VaR = P [ 1 exp( µ σz) ] past ER ( P) R SFRatio = σ P L Wiley

6 Meissner, Chapter 1 Meissner, Chapter 1 ρ realized = 2 n 2 n ρ ij, 2 ( ) = Wiley 3

7 Meissner, Chapter 2 Meissner, Chapter 2 S S = a( µ S ) t t 1 S t 1 Cov( ρt, ρt 1) AC( ρt, ρt 1) = σρ ( ) σρ ( ) t t Wiley

8 Meissner, Chapter 3 Meissner, Chapter 3 Correlation = cov( XY, ) σ σ X Y 2 6 di 1 2 nn ( 1). nc nd τ= nn ( 1)/ Wiley 5

9 Meissner, Chapter 4 Meissner, Chapter 4 p= P( Z < ζ) = Φ( ζ) where phi is the standard expression of the cumulative normal distribution and ζ is the log of the strike we subjectively set where we assume an asset will default Wiley

10 Tuckman, Chapter 6 Tuckman, Chapter 6 F R N N DV01 = F ˆβ R DV01 FaceValue FaceValue FirstHedge = SecondHedge FaceValue = FaceValue What Im hedging What Im hedging DV01 DV01 DV01 What Im Hedging FirstHedge β FirstHedge What Im Hedging Se β condhedge DV SecondHedge Wiley 7

11 Tuckman, Chapter 7 Tuckman, Chapter 7 r 1, 000, 000 cmt 2 k Wiley

12 Tuckman, Chapter 9 Tuckman, Chapter 9 dr =σdw dr = µ dt + σdw dr = k(θ r)dt+ σdw r 0 k( θ r0) = + / t σ dt dr = kr ( rdt ) + λdt+ σdw λ = k r + r dt dw k + σ θ λ r + k 2016 Wiley 9

13 Credit Risk Measurement and Management (CR)

14 de Servigny and Renault, Chapter 3 de Servigny and Renault, Chapter 3 S = VNk ( + σ T t) Ke Nk ( ) t t v rt ( t) 2016 Wiley 11

15 Stulz, Chapter 18 Stulz, Chapter 18 0 if AT K DTT (, ) = K = K max[ K AT, 0] K AT if AT < K Value of risky debt = Value of risk-free debt Value of put option on company assets rt ( t) S = A Nd ( ) Ke Nd ( ) t t 1 2 DtT) (, = AN( d ) + Ke N( d ) t 1 r( T t) 2 Credit spread = yd (t,t) yp(t,t) = λϒ Wiley

16 Malz, Chapter 6 Malz, Chapter 6 Probability of default = Prob(A T < K) = 1 Prob(A T K) = 1 N(e 2 ) e 1 ln A t 1 2 ut t) T t) K + ( + σ ( 2 = σ T t e = e σ T t 2 1 Expected loss = KN( e 2 ) A t e u(t t) N( e 1 ) Present value of expected loss = KP(t,T) D(t,T) This simplifies to Ke r(t t) N( d 2 )A t N( d 1 ) 2016 Wiley 13

17 Malz, Chapter 7 Malz, Chapter 7 Pt [ * < t] F() t = e λ 1 t F () t = λe λt Wiley

18 Malz, Chapter 8 Malz, Chapter 8 2 a i β i m β i i = + 1 i= 12,, Wiley 15

19 Gregory, Chapter 8 Gregory, Chapter 8 Nettingfactor = n+ n( n 1) ρ n Wiley

20 Gregory, Chapter 12 Gregory, Chapter 12 m CVA (1 Rec) DF(t i)ee( ti) PD( ti 1, ti). i= 1 F( u) = 1 exp( hu), h Spread (1 Recovery), Spread F(u) = (1 Recovery) u 1 exp. Incremental i m CVA = ( 1 Rec) DF(t )EE ( t, t ) PD(t, t ) j= 1 j i Incremental j 1 j j 1 j Wiley 17

21 Choudhry, Chapter 12 Choudhry, Chapter 12 CPR = 1 ( 1 SMM) % t, for t 30 months r = 60.%, for t > 30 months N Principalreceivedat Average life = t t t= 1 12 ( Totalprincipal) Wiley

22 Operational and Integrated Risk Management (OR)

23 Girling, Chapter 12 Girling, Chapter 12 N λ e fn ( ) = n! d Wiley

24 Crouhy, Chapter 17 Crouhy, Chapter 17 RAROC = Risk Adjusted Return Risk Adjusted Capital ARAROC = RAROC R f β e 2016 Wiley 21

25 Dowd, Chapter 14 Dowd, Chapter 14 LVaR = [ 1+ ( µ spread σspread )/2] VaR 1 ds = µ dt + σdw + dn L Wiley

26 Malz, Chapter 12 Malz, Chapter 12 e a d r = Lr ( L 1) r 1 ( s σs) 2 ( 1 + T)( 1+2T) 6T 2016 Wiley 23

27 Hull, Chapter 15 Hull, Chapter 15 Max( V, 0)+ al N i=1 wl M + wc i i j j i=1 max( Var, m * Var ) SRC t 1 c average + WCDR N N 1 PD i N 1 ( ) + ρ ( ) = 1 ρ EAD*LGD* WCDR EAD*LGD* PD EAD*LCG* ( WCDR PD )*MA 12. 5* EAD*LCG* ( WCDR PD )*MA Wiley

28 Hull, Chapter 16 Hull, Chapter 16 m * VaR +m * VaR c ave s stressed 2016 Wiley 25

29 Risk Management and Investment Management (IM)

30 Grinold and Kahn, Chapter 14 Grinold and Kahn, Chapter 14 λ A = IR 2. ψ P SC MCVA PC n n n 2016 Wiley 27

31 Jorion, Chapter 7 Jorion, Chapter 7 Portfolio VaR= VaRp = ασ p W = α x x VaR VaR cov(r ) VaRi = = = p Rp α σ, = α x w W w σ i i i p Wiley

32 Jorion, Chapter 17 Jorion, Chapter 17 R = R + R. = w R + ( w R W R ) asset polic ymix activemgt i b i b i i i i i b i b 2016 Wiley 29

33 Bodie, Kane, and Marcus, Chapter 24 Bodie, Kane, and Marcus, Chapter 24 Rp R Sharpe ratio = σ p f Rp R Treynor ratio = β p f α = R [ R + β ( R R )] p p f p m f α N τα ( ) = σ() e Wiley

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Risk Management and Financial Institutions

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