Tutorial_05_Finance.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Some Typical Financial Calculations\n",
    "\n",
    "This notebook showcases some classical finance calculations, which requires regressions, loops, root solving, optimisation and more. Details about these techniques are found in the other tutorials (notebooks).\n",
    "\n",
    "The notebook *(a)* estimates CAPM equations and autocorrelations; *(b)* implements a simple trading strategy; *(c)* calculates Value at Risk using a simple model for time-varying volatility; *(d)* calculates the Black-Scholes option price and implied volatility; *(e)* calculates and draws the mean-variance frontier."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Packages and Extra Functions\n",
    "\n",
    "The [Roots](https://github.com/JuliaMath/Roots.jl) package solves non-linear equations, [Distributions.jl](https://github.com/JuliaStats/Distributions.jl) defines distribution functions for a large number of distrunitions, and [StatsBase](https://github.com/JuliaStats/StatsBase.jl) has methods for estimating autocorrelations etc. The other packages are Standard Libraries (they come with the Julia installer)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Printf, Dates, DelimitedFiles, LinearAlgebra, Roots, Distributions, StatsBase\n",
    "\n",
    "include(\"src/printmat.jl\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots\n",
    "default(size = (480,320),fmt = :png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Load Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1979-01-01    10.190     4.180\n",
      "1979-02-01    -2.820    -3.410\n",
      "1979-03-01    10.900     5.750\n",
      "1979-04-01     2.470     0.050\n",
      "\n"
     ]
    }
   ],
   "source": [
    "x   = readdlm(\"Data/MyData.csv\",',',skipstart=1)        #monthly return data\n",
    "ym  = round.(Int,x[:,1])     #yearmonth, like 200712\n",
    "Rme = x[:,2]                 #market excess return\n",
    "Rf  = x[:,3]                 #interest rate\n",
    "R   = x[:,4]                 #return on small growth stocks\n",
    "Re  = R - Rf                 #excess returns\n",
    "T   = size(Rme,1)\n",
    "\n",
    "dN = Date.(string.(ym),\"yyyymm\")  #convert to string and then Julia Date\n",
    "printmat(dN[1:4],Re[1:4],Rme[1:4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CAPM\n",
    "\n",
    "The CAPM regression is\n",
    "\n",
    "$R_{t}^{e}  =\\alpha+\\beta R_{mt}^{e}+\\varepsilon_{t}$,\n",
    "\n",
    "where $R_{t}^{e}$ is the excess return of test asset and $R_{mt}^{e}$ is the market excess return. Theory says that $\\alpha=0$, which is easily tested.\n",
    "\n",
    "### A Remark on the Code\n",
    "- The OLS coeffcients on the regressors in `x` are called `b` in the code below. Given the way `x` is defined, `b[1]` corresponds to $\\alpha$ and `b[2]` to $\\beta$.\n",
    "- There are clearly packages that can do OLS, but we do not use them here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1mRegression results:\u001b[22m\u001b[39m\n",
      "\n",
      "      coeff       std    t-stat\n",
      "α    -0.504     0.304    -1.656\n",
      "β     1.341     0.066    20.427\n",
      "\n",
      "      R2:      0.519\n",
      "no. of observations:    388    \n"
     ]
    }
   ],
   "source": [
    "x    = [ones(T) Rme]             #regressors\n",
    "y    = copy(Re)                  #to get standard OLS notation\n",
    "b    = x\\y                       #OLS, intercept and slope\n",
    "u    = y - x*b                   #residuals\n",
    "covb = inv(x'x)*var(u)           #cov(b), see any textbook\n",
    "stdb = sqrt.(diag(covb))         #std(b)\n",
    "R2   = 1 - var(u)/var(y)\n",
    "\n",
    "printblue(\"Regression results:\\n\")\n",
    "printmat([b stdb b./stdb],colNames=[\"coeff\",\"std\",\"t-stat\"],rowNames=[\"α\",\"β\"])\n",
    "printlnPs(\"R2: \",R2)\n",
    "printlnPs(\"no. of observations: \",T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Return Autocorrelation\n",
    "\n",
    "That is, the correlation of $R_{t}^{e}$ and $R_{t-s}^{e}$. \n",
    "\n",
    "It can be shown that the t-stat of an autocorrelation is $\\sqrt{T}$ times the autocorrelation.\n",
    "\n",
    "### A Remark on the Code\n",
    "- `autocor(Re,plags)` from the `StatsBase` package estimates the autocorrelations for the lags defines in the rang (or vector) `plags`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1mAutocorrelations:\u001b[22m\u001b[39m\n",
      "\n",
      "lag  autocorr    t-stat\n",
      "1       0.216     4.253\n",
      "2       0.002     0.046\n",
      "3      -0.018    -0.359\n",
      "4      -0.065    -1.289\n",
      "5      -0.027    -0.536\n",
      "\n"
     ]
    }
   ],
   "source": [
    "plags = 1:5\n",
    "ρ = autocor(Re,plags)         #using the StatsBase package\n",
    "\n",
    "printblue(\"Autocorrelations:\\n\")\n",
    "printmat([ρ sqrt(T)*ρ],colNames=[\"autocorr\",\"t-stat\"],rowNames=string.(plags),cell00=\"lag\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A Trading Strategy\n",
    "\n",
    "The next cell implements a very simple momentum trading strategy. \n",
    "\n",
    "1. If $R_{t-1}^{e}\\ge0$, then we hold the market index and shorten the riskfree from $t-1$ to $t$. This means that we will earn $R_{t}^{e}$.\n",
    "\n",
    "2. Instead,  if $R_{t-1}^{e}<0$, then we do the opposite. This means that we will earn $-R_{t}^{e}$. \n",
    "\n",
    "This simple strategy could be coded without using a loop, but \"vectorization\" does not speed up much.\n",
    "\n",
    "We compare with a \"passive\" portfolio, which is just holding the asset all the time (and earning $R_{t}^{e}$ in each period)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1mThe annualized mean excess return and Sharpe ratios of the strategy and a passive portfolio:\u001b[22m\u001b[39m\n",
      "\n",
      "      strategy   passive\n",
      "mean    26.733     3.329\n",
      "SR       0.932     0.112\n",
      "\n"
     ]
    }
   ],
   "source": [
    "(w,Rp)  = (fill(NaN,T),fill(NaN,T))\n",
    "for t = 2:T\n",
    "  w[t]  = ifelse(Re[t-1] < 0,-1,1)         #w is -1 or 1\n",
    "  Rp[t] = w[t]*Re[t]\n",
    "end\n",
    "\n",
    "R_all = hcat(Rp[2:end],Re[2:end])          #Tx2, matrix of both returns\n",
    "μ     = mean(R_all,dims=1)\n",
    "σ     = std(R_all,dims=1)\n",
    "\n",
    "printblue(\"The annualized mean excess return and Sharpe ratios of the strategy and a passive portfolio:\\n\")\n",
    "xx = [μ*12;sqrt(12)*μ./σ]\n",
    "printmat(xx;rowNames=[\"mean\",\"SR\"],colNames=[\"strategy\",\"passive\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Value at Risk\n",
    "\n",
    "The next cell constructs an simple estimate of $\\sigma_t^2$ as a backward looking moving average:\n",
    "\n",
    "$\\sigma_t^2 = \\lambda \\sigma_{t-1}^2 + (1-\\lambda) (R_{t-1}^e -\\mu_{t-1})^2$,\n",
    "where $\\mu_{t}=\\lambda \\mu_{t-1} + (1-\\lambda) R_{t-1}^e$\n",
    "\n",
    "Then, we calculate the 95% VaR by assuming a N$(\\mu,\\sigma_t^2)$ distribution:\n",
    "\n",
    "$\\textrm{VaR}_{t} = - (\\mu_t-1.64\\sigma_t)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "(μ₀,σ₀) = (0.5,5.0)          #some starting values for obs t=0\n",
    "\n",
    "λ = 0.94\n",
    "(μ,σ²) = (fill(μ₀,T),fill(σ₀^2,T))    #vectors, time-varying mean and variance\n",
    "for t in 2:T\n",
    "    μ[t]  = λ*μ[t-1]  + (1-λ)*Rme[t-1]\n",
    "    σ²[t] = λ*σ²[t-1] + (1-λ)*(Rme[t-1]-μ[t-1])^2    #RiskMetrics approach\n",
    "end\n",
    "\n",
    "VaR95 = -(μ .- 1.64*sqrt.(σ²));      #VaR at 95% level"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xTicksLoc = [Date(1980);Date(1990);Date(2000);Date(2010)]\n",
    "xTicksLab = Dates.format.(xTicksLoc,\"Y\")\n",
    "\n",
    "p1 = plot( dN,VaR95,\n",
    "           color = :blue,\n",
    "           legend = false,\n",
    "           xticks = (xTicksLoc,xTicksLab),\n",
    "           ylim = (0,11),\n",
    "           title = \"1-month Value at Risk (95%)\",\n",
    "           ylabel = \"%\",\n",
    "           annotation = (Date(1982),1,text(\"(for US equity market)\",8,:left)) )\n",
    "display(p1)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Options\n",
    "\n",
    "## Black-Scholes Option Price\n",
    "\n",
    "Let $S$ be the the current spot price of an asset and $y$ be the interest rate.\n",
    "\n",
    "The Black-Scholes formula for a European call option with strike price $K$ and time to expiration $m$ is\n",
    "\n",
    "$C  =S\\Phi(d_{1})  -e^{-ym}K\\Phi(d_{2})$, where\n",
    "\n",
    "$d_{1} =\\frac{\\ln(S/K)+(y+\\sigma^{2}/2)m}{\\sigma\\sqrt{m}} \\ \\text{ and } \\ d_{2}=d_{1}-\\sigma\\sqrt{m}$ \n",
    "\n",
    "and where $\\Phi(d)$ denotes the probability of $x\\leq d$ when $x$ has an $N(0,1)$ distribution. All variables except the volatility ($\\sigma$) are directly observable.\n",
    "\n",
    "### A Remark on the Code\n",
    "- `cdf(Normal(0,1),x)` defines the cdf of a N$(0,1)$ distribution, using the `Distributions.jl` package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "OptionBlackSPs"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Pr(z<=x) for N(0,1)\n",
    "\"\"\"\n",
    "Φ(x) = cdf(Normal(0,1),x)     #a one-line function, to get standard notation\n",
    "\n",
    "\n",
    "\"\"\"\n",
    "Calculate Black-Scholes european call option price\n",
    "\"\"\"\n",
    "function OptionBlackSPs(S,K,m,y,σ)\n",
    "\n",
    "  d1 = ( log(S/K) + (y+1/2*σ^2)*m ) / (σ*sqrt(m))\n",
    "  d2 = d1 - σ*sqrt(m)\n",
    "  c  = S*Φ(d1) - exp(-y*m)*K*Φ(d2)\n",
    "  return c\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          \n",
      "call price according to Black-Scholes for a single K value:      1.358\n"
     ]
    }
   ],
   "source": [
    "σ = 0.4\n",
    "c1 = OptionBlackSPs(10,10,0.5,0.1,σ)         #call price for a single K value\n",
    "printlnPs(\"\\n\",\"call price according to Black-Scholes for a single K value: \",c1)\n",
    "\n",
    "K = range(7,13,length=51)                    #call prices for several K values\n",
    "c = OptionBlackSPs.(10,K,0.5,0.1,σ);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p1 = plot( K,c,\n",
    "           color = :red,\n",
    "           legend = false,\n",
    "           title = \"Black-Scholes call option price\",\n",
    "           xlabel = \"strike price\",\n",
    "           ylabel = \"option price\",\n",
    "           annotation = (10,3,text(\"S=10, m=1/2, y=0.1\",8,:left)) )\n",
    "display(p1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Implied Volatility\n",
    "\n",
    "...is the $\\sigma$ value that makes the Black-Scholes equation give the same option price as observed on the market. It is often interpreted as the \"market uncertainty.\"\n",
    "\n",
    "The next cell uses the call option price calculated above as the market price. The implied volatility should then equal the volatility used above (this is a way to check your coding).\n",
    "\n",
    "The subsequent cells instead use some data on options on German government bonds and calculate the $\\sigma$ for each of them.`\n",
    "\n",
    "### A Remark on the Code\n",
    "- the `find_zero()` function from the `Roots.jl` package solve a non-linear function for its root (in terms of one of the inputs of the function). In the cell below, we thus solve for the `σ` value that makes `OptionBlackSPs(10,10,0.5,0.1,σ)-c1` equal to zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Implied volatility:      0.400, compare with: 0.4\n"
     ]
    }
   ],
   "source": [
    "                                #solve for implied vol\n",
    "iv = find_zero(σ->OptionBlackSPs(10,10,0.5,0.1,σ)-c1,(0.00001,5))\n",
    "\n",
    "printlnPs(\"Implied volatility: \",iv,\", compare with: $σ\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "21"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  LIFFE Bunds option data, trade date April 6, 1994\n",
    "K = [                        #strike prices\n",
    "      92.00;  94.00;  94.50;  95.00;  95.50;  96.00;  96.50;  97.00;\n",
    "      97.50;  98.00;  98.50;  99.00;  99.50;  100.0;  100.5;  101.0;\n",
    "     101.5;  102.0;  102.5;  103.0;  103.5 ];\n",
    "C = [                        #call prices\n",
    "      5.13;    3.25;    2.83;    2.40;    2.00;    1.64;    1.31;    1.02;\n",
    "      0.770;   0.570;   0.400;   0.280;   0.190;   0.130;  0.0800;  0.0500;\n",
    "      0.0400;  0.0300;  0.0200;  0.0100;  0.0100 ];\n",
    "S = 97.05                #spot price\n",
    "m = 48/365               #time to expiry in years\n",
    "y = 0.0                  #Interest rate: LIFFE=>no discounting\n",
    "N = length(K)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1mFrom Bunds options data:\u001b[22m\u001b[39m\n",
      "\n",
      "    strike         σ\n",
      "    92.000     0.094\n",
      "    94.000     0.081\n",
      "    94.500     0.081\n",
      "    95.000     0.078\n",
      "    95.500     0.075\n",
      "    96.000     0.074\n",
      "    96.500     0.072\n",
      "    97.000     0.071\n",
      "    97.500     0.070\n",
      "    98.000     0.069\n",
      "    98.500     0.068\n",
      "    99.000     0.067\n",
      "    99.500     0.067\n",
      "   100.000     0.068\n",
      "   100.500     0.067\n",
      "   101.000     0.067\n",
      "   101.500     0.070\n",
      "   102.000     0.073\n",
      "   102.500     0.074\n",
      "   103.000     0.072\n",
      "   103.500     0.077\n",
      "\n"
     ]
    }
   ],
   "source": [
    "iv = fill(NaN,N)       #looping over strikes\n",
    "for i in 1:N\n",
    "  iv[i] = find_zero(sigma->OptionBlackSPs(S,K[i],m,y,sigma)-C[i],(0.00001,5))\n",
    "end\n",
    "\n",
    "printblue(\"From Bunds options data:\\n\")\n",
    "printmat(K,iv,colNames=[\"strike\",\"σ\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p1 = plot( K,iv,\n",
    "           color = :red,\n",
    "           legend =false,\n",
    "           title = \"Implied volatility\",\n",
    "           xlabel = \"strike price\",\n",
    "           annotation = (98,0.09,text(\"Bunds options April 6, 1994\",8,:left)) )\n",
    "display(p1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mean-Variance Frontier\n",
    "\n",
    "Given a vector of average returns ($\\mu$) and a variance-covariance matrix ($\\Sigma$), the mean-variance frontier shows the lowest possible portfolio uncertainty for a given expected portfolio return (denoted `μˣ` below).\n",
    "\n",
    "It is thus the solution to a quadratic minimization problem. The cells below will use matrix formulas for this solution, but we often have to resort to numerical methods (especially when there are portfolio restrictions).\n",
    "\n",
    "The mean-variance frontier is typically plotted with the portfolio standard deviation (*not* the variance) on the horizontal axis and the portfolio expected return $\\mu\\text{star}$ on the vertical axis.\n",
    "\n",
    "We calculate and plot two different mean-variance frontiers: *(1)* when we only consider risky assets; *(2)* when we also consider a risk-free asset.\n",
    "\n",
    "### A Remark on the Code\n",
    "The calculations for the mean-variance frontiers are in two functions (for the case of only risky assets, and for risky and a riskfree asset). The calculations involve solving a system of linear equations (or calculating a matrix inverse) for each value of the expected return `μˣ`. To speed up the calculations we use the `factorize()` function from the `LinearAlgebra` standard library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "μ: \n",
      "     0.115\n",
      "     0.095\n",
      "     0.060\n",
      "\n",
      "Σ: \n",
      "     0.017     0.003     0.006\n",
      "     0.003     0.006     0.000\n",
      "     0.006     0.000     0.010\n",
      "\n",
      "Rf: \n",
      "     0.030\n",
      "\n"
     ]
    }
   ],
   "source": [
    "μ = [11.5, 9.5, 6]/100          #expected returns\n",
    "Σ  = [166  34  58;              #covariance matrix\n",
    "       34  64   4;\n",
    "       58   4 100]/100^2\n",
    "Rf = 0.03                       #riskfree return (an interest rate)\n",
    "\n",
    "println(\"μ: \")\n",
    "printmat(μ)\n",
    "println(\"Σ: \")\n",
    "printmat(Σ)\n",
    "println(\"Rf: \")\n",
    "printmat(Rf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MVCalcRf"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "    MVCalc(μˣ,μ,Σ)\n",
    "\n",
    "Calculate the std and weights of a portfolio (with mean return μˣ) on MVF of risky assets.\n",
    "\n",
    "# Input\n",
    "- `μˣ::Vector`:    K vector, mean returns to calculate results for\n",
    "- `μ::Vector`:     n vector, mean returns\n",
    "- `Σ::Matrix`:     nxn, covariance matrix of returns, can contain riskfree assets\n",
    "\n",
    "# Output\n",
    "- `StdRp::Vector`:    K vector, standard deviation of mean-variance portfolio (risky only) with mean μˣ\n",
    "- `w_p::Matrix`:      Kxn, portfolio weights of       \"\"\n",
    "\n",
    "\"\"\"\n",
    "function MVCalc(μˣ,μ,Σ) #the std of a portfolio on MVF of risky assets\n",
    "    (K,n) = (length(μˣ),length(μ))\n",
    "    A = [Σ        μ ones(n);   #A is just a name of this matrix, it's not asset A\n",
    "         μ'       0 0;\n",
    "         ones(n)' 0 0];\n",
    "    Af = factorize(A)          #factorize so we can solve wλδ_i repeatedly (and fast)\n",
    "    (w,StdRp) = (fill(NaN,K,n),fill(NaN,K))\n",
    "    for i in 1:K                #loop over μˣ[i]\n",
    "        wλδ_i    = Af\\[zeros(n);μˣ[i];1]\n",
    "        w_i      = wλδ_i[1:n]\n",
    "        StdRp[i] = sqrt(w_i'Σ*w_i)\n",
    "        w[i,:]   = w_i\n",
    "    end\n",
    "    return StdRp,w\n",
    "end\n",
    "\n",
    "\n",
    "\"\"\"\n",
    "Calculate the std of a portfolio (with mean μˣ) on MVF of (Risky,Riskfree)\n",
    "\"\"\"\n",
    "function MVCalcRf(μˣ,μ,Σ,Rf)\n",
    "    (K,n) = (length(μˣ),length(μ))\n",
    "    μᵉ = μ .- Rf\n",
    "    A  = [Σ   μᵉ;\n",
    "          μᵉ' 0]\n",
    "    Af = factorize(A)\n",
    "    (w,StdRp) = (fill(NaN,K,n),fill(NaN,K))\n",
    "    for i in 1:K\n",
    "      wλ_i     = Af\\[zeros(n);(μˣ[i]-Rf)]\n",
    "      w_i      = wλ_i[1:n]\n",
    "      StdRp[i] = sqrt(w_i'Σ*w_i)\n",
    "      w[i,:]   = w_i\n",
    "    end\n",
    "    return StdRp,w\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "μˣ = range(Rf,0.15,length=201)\n",
    "L     = length(μˣ)\n",
    "\n",
    "StdRp = MVCalc(μˣ,μ,Σ)[1];    #risky assets only, [1] to get the first output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p1 = plot( StdRp*100,μˣ*100,\n",
    "           linecolor = :red,\n",
    "           xlim = (0,15),\n",
    "           ylim = (0,15),\n",
    "           label = \"MVF\",\n",
    "           legend = :topleft,\n",
    "           title = \"MVF, only risky assets\",\n",
    "           xlabel = \"Std(Rp), %\",\n",
    "           ylabel = \"ERp, %\" )\n",
    "scatter!(sqrt.(diag(Σ))*100,μ*100,color=:red,label=\"assets\")\n",
    "display(p1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "StdRpRf = MVCalcRf(μˣ,μ,Σ,Rf)[1];         #with riskfree too"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p1 = plot( [StdRp StdRpRf]*100,[μˣ μˣ]*100,\n",
    "           legend = nothing,\n",
    "           linestyle = [:solid :dash],\n",
    "           linecolor = [:red :blue],\n",
    "           xlim = (0,15),\n",
    "           ylim = (0,15),\n",
    "           title = \"MVF, risky and riskfree assets\",\n",
    "           xlabel = \"Std(Rp), %\",\n",
    "           ylabel = \"ERp, %\" )\n",
    "scatter!(sqrt.(diag(Σ))*100,μ*100,color=:red)\n",
    "display(p1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "@webio": {
   "lastCommId": null,
   "lastKernelId": null
  },
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Julia 1.11.1",
   "language": "julia",
   "name": "julia-1.11"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.11.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}