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% Document Info
\author{Spazztaco}
\pdfinfo{
  /Title (coec-371.pdf)
  /Creator (Cheatography)
  /Author (Spazztaco)
  /Subject (Coec 371 Cheat Sheet)
}

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\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
    \SetRowColor{DarkBackground}
    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Coec 371 Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Spazztaco} via \textcolor{DarkBackground}{\uline{cheatography.com/95917/cs/20777/}}}
\end{tabulary}
\end{multicols}}

\fancyfoot[L]{ \footnotesize
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
  \SetRowColor{FootBackground}
  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}Spazztaco \\
  \uline{cheatography.com/spazztaco} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 15th October, 2019.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
  \SetRowColor{white}
  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
\raggedright
\raggedcolumns

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% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.

\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Formula}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Price of Longer Maturity Coupon Paying Bond} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{P = c/r*(1 - 1/(1+r)\textasciicircum{}t\textasciicircum{} ) + ParValue/(1+r)\textasciicircum{}t\textasciicircum{}} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Price of Zero Coupon Bond} \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{P = ParValue/(1+r)\textasciicircum{}t\textasciicircum{}} \tn 
% Row Count 4 (+ 1)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Price of Short Maturity Coupon Paying Bond} \tn 
% Row Count 5 (+ 1)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{P = Coupon/(1+r)\textasciicircum{}t\textasciicircum{} + (ParValue+Coupon)/(1+r)\textasciicircum{}t\textasciicircum{}} \tn 
% Row Count 6 (+ 1)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Nominal Growth rate of Cash Flows} \tn 
% Row Count 7 (+ 1)
% Row 7
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{i = \seqsplit{(1+GrowthRate)*(1+InflationRate)} - 1} \tn 
% Row Count 8 (+ 1)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Real Return Adjusted for Inflation} \tn 
% Row Count 9 (+ 1)
% Row 9
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{r = (1+i)/(1+Inflation)} \tn 
% Row Count 10 (+ 1)
% Row 10
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Present Value of Cash Flows} \tn 
% Row Count 11 (+ 1)
% Row 11
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{PV = Cash * ((1+i)\textasciicircum{}t-1\textasciicircum{}/(1+DiscountRate)\textasciicircum{}t-1\textasciicircum{}+(1+i)\textasciicircum{}t\textasciicircum{}/(1+DiscountRate)\textasciicircum{}t\textasciicircum{} +...)} \tn 
% Row Count 13 (+ 2)
% Row 12
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Computing YTM} \tn 
% Row Count 14 (+ 1)
% Row 13
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Rates = Flat; Rates = YTM. \{\{nl\}\}\{\{nl\}\}	 Rates =/= Flat; Solve for Price, Swap Rates for Y and solve for Y} \tn 
% Row Count 17 (+ 3)
% Row 14
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Discount Factors (D) for Zero Coupon Bonds} \tn 
% Row Count 18 (+ 1)
% Row 15
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Price/100} \tn 
% Row Count 19 (+ 1)
% Row 16
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Discount Factor (D) for Coupon Paying Bonds} \tn 
% Row Count 20 (+ 1)
% Row 17
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Price = C*D{[}1{]} + (ParValue+C)D{[}2{]}} \tn 
% Row Count 21 (+ 1)
% Row 18
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Calculation for Spot Rates Using Discount Factor} \tn 
% Row Count 22 (+ 1)
% Row 19
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{r = (1/D)/\textasciicircum{}T\textasciicircum{} -1  \{\{nl\}\}\{\{nl\}\}	 For semiannual multiply answer by 2} \tn 
% Row Count 24 (+ 2)
% Row 20
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Calculating Price with Discount Rates} \tn 
% Row Count 25 (+ 1)
% Row 21
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{P = C*D{[}1{]} + C*D{[}2{]} + (ParValue+C)D{[}3{]}  \{\{nl\}\}\{\{nl\}\}		For semiannual C/2} \tn 
% Row Count 27 (+ 2)
% Row 22
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Macaulay Definition} \tn 
% Row Count 28 (+ 1)
% Row 23
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{D = (1+r)/r - \{{[}(1+r) + T(C-R){]} / (C{[}(1+r)\textasciicircum{}T\textasciicircum{} - 1{]} +r)\} \{\{nl\}\}\{\{nl\}\}	 Where R = Flat Rate Or YTM. \{\{nl\}\}	When Semiannual r/2 and c/2, divide final answer by 2} \tn 
% Row Count 32 (+ 4)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Formula (cont)}}  \tn
% Row 24
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Modified Duration} \tn 
% Row Count 1 (+ 1)
% Row 25
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{D*= D/1+r} \tn 
% Row Count 2 (+ 1)
% Row 26
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Present Value of Liabilities} \tn 
% Row Count 3 (+ 1)
% Row 27
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Liabilities * 1/(1+r)\textasciicircum{}T\textasciicircum{}} \tn 
% Row Count 4 (+ 1)
% Row 28
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Compute Realized Returns} \tn 
% Row Count 5 (+ 1)
% Row 29
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{( P{[}0{]} - P{[}-1{]} )/ P{[}-1{]}} \tn 
% Row Count 6 (+ 1)
% Row 30
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Computing Expected Returns} \tn 
% Row Count 7 (+ 1)
% Row 31
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{E(R) = (Probability * Return + ...)} \tn 
% Row Count 8 (+ 1)
% Row 32
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Computing Standard Deviation} \tn 
% Row Count 9 (+ 1)
% Row 33
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Sd(R) = Sqrt(Probability*(Return - E(R)\textasciicircum{}2\textasciicircum{} +...)} \tn 
% Row Count 10 (+ 1)
% Row 34
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Effective Annual Rate (EAR)} \tn 
% Row Count 11 (+ 1)
% Row 35
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{P{[}1{]}*(1+EAR)\textasciicircum{}T\textasciicircum{} = P{[}T{]}} \tn 
% Row Count 12 (+ 1)
% Row 36
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Converting Monthly APR to Semiannual} \tn 
% Row Count 13 (+ 1)
% Row 37
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{(1+APR/12)\textasciicircum{}6\textasciicircum{} -1} \tn 
% Row Count 14 (+ 1)
% Row 38
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Calculating for Spot Rates using Price Formula} \tn 
% Row Count 15 (+ 1)
% Row 39
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Price = ParValue/(1+r) then solve for r} \tn 
% Row Count 16 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Descriptive}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Constructing an Arbitage} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{e.g: \{\{nl\}\} Year 1 =\textgreater{} 100x{[}1{]} +5x{[}2{]} = 7 \{x{[}3{]}\} \{\{nl\}\} \{\{nl\}\}Year 2 =\textgreater{} 105x{[}2{]} = 107 \{x{[}3{]}\} \{\{nl\}\} \{\{nl\}\} Solve for x{[}1{]} and x{[}2{]}} \tn 
% Row Count 4 (+ 3)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Computing Realized Returns assuming Dividend Reinvesting} \tn 
% Row Count 6 (+ 2)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{e.g: \{\{nl\}\} Invest \$1000, 1000/Share Price = \# of Shares \{\{nl\}\} \{\{nl\}\} \# of Shares + {[}\# of Shares*DividendPayout{]}/NextSharePrice \{\{nl\}\} \{\{nl\}\} Repeat til end of Periods, compute the realized returns} \tn 
% Row Count 10 (+ 4)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Monthly Payment Questions} \tn 
% Row Count 11 (+ 1)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Owed Amount = c/r*{[}1-1/(1+r)\textasciicircum{}T\textasciicircum{}{]} \{\{nl\}\} \{\{nl\}\} Solve for C, Make sure T is in the right format (Monthly Payments, Yearly, Daily)} \tn 
% Row Count 14 (+ 3)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{What is your return if term structure remains flat and you hold for X years? \{\{nl\}\} TSR = Term Structure Rate} \tn 
% Row Count 17 (+ 3)
% Row 7
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{(1+r)\textasciicircum{}T\textasciicircum{} = R/100 \{\{nl\}\} \{\{nl\}\} R = C*(1+TSR)\textasciicircum{}T-1\textasciicircum{} + C*(1+TSR)\textasciicircum{}T-2\textasciicircum{} +... ...+ C*(1+TSR)\textasciicircum{}1\textasciicircum{} + (ParValue + C) \{\{nl\}\}\{\{nl\}\} Plug in R to first equation then solve for small r} \tn 
% Row Count 21 (+ 4)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Simple Trading Model}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Expected Value of Stock} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{E(V) = P{[}h{]}*V{[}h{]} + P{[}l\}*V{[}l{]}} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Ask price so Market Maker breaks even} \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{A = \{\{nl\}\}	  ( P{[}u{]}*P{[}l{]}*V{[}l{]} + P{[}h{]}*V{[}h{]} ) / ( P{[}u{]}*P{[}l{]}+ P{[}h\} )} \tn 
% Row Count 5 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Bid price so Market Maker breaks even} \tn 
% Row Count 6 (+ 1)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{B = \{\{nl\}\}	( P{[}l{]}*V{[}l{]} + P{[}u{]}*P{[}h{]}*V{[}h{]} ) / ( P{[}l{]} + P{[}u{]}*P{[}h{]}} \tn 
% Row Count 8 (+ 2)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Bid-Ask Spread} \tn 
% Row Count 9 (+ 1)
% Row 7
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{s = A - B} \tn 
% Row Count 10 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Note}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Note: Spot Rates = Flat Term Rate. \newline % Row Count 1 (+ 1)
And Equal to YTM if the rates are flat.  \newline % Row Count 2 (+ 1)
If not, YTM is found using the formula to your left.% Row Count 4 (+ 2)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}