$$ % Typography and symbols \newcommand{\msf}[1]{\mathsf{#1}} \newcommand{\ctx}{\Gamma} \newcommand{\qamp}{&\quad} \newcommand{\qqamp}{&&\quad} \newcommand{\Coloneqq}{::=} \newcommand{\proves}{\vdash} \newcommand{\star}[1]{#1^{*}} \newcommand{\eps}{\varepsilon} \newcommand{\nul}{\varnothing} \newcommand{\brc}[1]{\{{#1}\}} \newcommand{\binopm}[2]{#1~\bar{\oplus}~#2} \newcommand{\mag}[1]{|{#1}|} \newcommand{\aequiv}{\equiv_\alpha} \newcommand{\semi}[2]{{#1};~{#2}} % Untyped lambda calculus \newcommand{\fun}[2]{\lambda ~ {#1} ~ . ~ {#2}} \newcommand{\app}[2]{#1 ~ #2} \newcommand{\fix}[3]{\msf{fix}~({#1} : {#2}) ~ . ~ #3 } \newcommand{\truet}{\msf{true}} \newcommand{\falset}{\msf{false}} \newcommand{\define}[2]{{#1} \triangleq {#2}} % Typed lambda calculus - expressions \newcommand{\funt}[3]{\lambda ~ \left(#1 : #2\right) ~ . ~ #3} \newcommand{\lett}[4]{\msf{let} ~ \hasType{#1}{#2} = #3 ~ \msf{in} ~ #4} \newcommand{\letrec}[4]{\msf{letrec} ~ \hasType{#1}{#2} = #3 ~ \msf{in} ~ #4}a \newcommand{\ift}[3]{\msf{if} ~ {#1} ~ \msf{then} ~ {#2} ~ \msf{else} ~ {#3}} \newcommand{\rec}[5]{\msf{rec}(#1; ~ #2.#3.#4)(#5)} \newcommand{\case}[5]{\msf{case} ~ {#1} ~ \{ L(#2) \to #3 \mid R(#4) \to #5 \}} \newcommand{\pair}[2]{\left({#1},~{#2}\right)} \newcommand{\proj}[2]{#1 . #2} \newcommand{\inj}[3]{\msf{inj} ~ #1 = #2 ~ \msf{as} ~ #3} \newcommand{\letv}[3]{\msf{let} ~ {#1} = {#2} ~ \msf{in} ~ {#3}} \newcommand{\fold}[2]{\msf{fold}~{#1}~\msf{as}~{#2}} \newcommand{\unfold}[1]{\msf{unfold}~{#1}} \newcommand{\poly}[2]{\Lambda~{#1}~.~ #2} \newcommand{\polyapp}[2]{{#1}~\left[{#2}\right]} \newcommand{\export}[3]{\msf{export}~ #1 ~\msf{without}~{#2}~\msf{as}~ #3} \newcommand{\import}[4]{\msf{import} ~ ({#1}, {#2}) = {#3} ~ \msf{in} ~ #4} % Typed lambda calculus - types \newcommand{\tnum}{\msf{num}} \newcommand{\tstr}{\msf{string}} \newcommand{\tint}{\msf{int}} \newcommand{\tbool}{\msf{bool}} \newcommand{\tfun}[2]{#1 \rightarrow #2} \newcommand{\tprod}[2]{#1 \times #2} \newcommand{\tsum}[2]{#1 + #2} \newcommand{\trec}[2]{\mu~{#1}~.~{#2}} \newcommand{\tvoid}{\msf{void}} \newcommand{\tunit}{\msf{unit}} \newcommand{\tpoly}[2]{\forall~{#1}~.~{#2}} \newcommand{\tmod}[2]{\exists ~ {#1} ~ . ~ #2} % WebAssembly \newcommand{\wconst}[1]{\msf{i32.const}~{#1}} \newcommand{\wbinop}[1]{\msf{i32}.{#1}} \newcommand{\wgetlocal}[1]{\msf{get\_local}~{#1}} \newcommand{\wsetlocal}[1]{\msf{set\_local}~{#1}} \newcommand{\wgetglobal}[1]{\msf{get\_global}~{#1}} \newcommand{\wsetglobal}[1]{\msf{set\_global}~{#1}} \newcommand{\wload}{\msf{i32.load}} \newcommand{\wstore}{\msf{i32.store}} \newcommand{\wsize}{\msf{memory.size}} \newcommand{\wgrow}{\msf{memory.grow}} \newcommand{\wunreachable}{\msf{unreachable}} \newcommand{\wblock}[1]{\msf{block}~{#1}} \newcommand{\wloop}[1]{\msf{loop}~{#1}} \newcommand{\wbr}[1]{\msf{br}~{#1}} \newcommand{\wbrif}[1]{\msf{br\_if}~{#1}} \newcommand{\wreturn}{\msf{return}} \newcommand{\wcall}[1]{\msf{call}~{#1}} \newcommand{\wlabel}[2]{\msf{label}~\{#1\}~{#2}} \newcommand{\wframe}[2]{\msf{frame}~({#1}, {#2})} \newcommand{\wtrapping}{\msf{trapping}} \newcommand{\wbreaking}[1]{\msf{breaking}~{#1}} \newcommand{\wreturning}[1]{\msf{returning}~{#1}} \newcommand{\wconfig}[5]{\{\msf{module}{:}~{#1};~\msf{mem}{:}~{#2};~\msf{locals}{:}~{#3};~\msf{stack}{:}~{#4};~\msf{instrs}{:}~{#5}\}} \newcommand{\wfunc}[4]{\{\msf{params}{:}~{#1};~\msf{locals}{:}~{#2};~\msf{return}~{#3};~\msf{body}{:}~{#4}\}} \newcommand{\wmodule}[1]{\{\msf{funcs}{:}~{#1}\}} \newcommand{\wcg}{\msf{globals}} \newcommand{\wcf}{\msf{funcs}} \newcommand{\wci}{\msf{instrs}} \newcommand{\wcs}{\msf{stack}} \newcommand{\wcl}{\msf{locals}} \newcommand{\wclab}{\msf{labels}} \newcommand{\wcm}{\msf{mem}} \newcommand{\wcmod}{\msf{module}} \newcommand{\wsteps}[2]{\steps{\brc{#1}}{\brc{#2}}} \newcommand{\with}{\underline{\msf{with}}} \newcommand{\wvalid}[2]{{#1} \vdash {#2}~\msf{valid}} \newcommand{\wif}[2]{\msf{if}~{#1}~{\msf{else}}~{#2}} \newcommand{\wfor}[4]{\msf{for}~(\msf{init}~{#1})~(\msf{cond}~{#2})~(\msf{post}~{#3})~{#4}} % assign4.3 custom \newcommand{\wtry}[2]{\msf{try}~{#1}~\msf{catch}~{#2}} \newcommand{\wraise}{\msf{raise}} \newcommand{\wraising}[1]{\msf{raising}~{#1}} \newcommand{\wconst}[1]{\msf{i32.const}~{#1}} \newcommand{\wbinop}[1]{\msf{i32}.{#1}} \newcommand{\wgetlocal}[1]{\msf{get\_local}~{#1}} \newcommand{\wsetlocal}[1]{\msf{set\_local}~{#1}} \newcommand{\wgetglobal}[1]{\msf{get\_global}~{#1}} \newcommand{\wsetglobal}[1]{\msf{set\_global}~{#1}} \newcommand{\wload}{\msf{i32.load}} \newcommand{\wstore}{\msf{i32.store}} \newcommand{\wsize}{\msf{memory.size}} \newcommand{\wgrow}{\msf{memory.grow}} \newcommand{\wunreachable}{\msf{unreachable}} \newcommand{\wblock}[1]{\msf{block}~{#1}} \newcommand{\wloop}[1]{\msf{loop}~{#1}} \newcommand{\wbr}[1]{\msf{br}~{#1}} \newcommand{\wbrif}[1]{\msf{br\_if}~{#1}} \newcommand{\wreturn}{\msf{return}} \newcommand{\wcall}[1]{\msf{call}~{#1}} \newcommand{\wlabel}[2]{\msf{label}~\{#1\}~{#2}} \newcommand{\wframe}[2]{\msf{frame}~({#1}, {#2})} \newcommand{\wtrapping}{\msf{trapping}} \newcommand{\wbreaking}[1]{\msf{breaking}~{#1}} \newcommand{\wreturning}[1]{\msf{returning}~{#1}} \newcommand{\wconfig}[5]{\{\msf{module}{:}~{#1};~\msf{mem}{:}~{#2};~\msf{locals}{:}~{#3};~\msf{stack}{:}~{#4};~\msf{instrs}{:}~{#5}\}} \newcommand{\wfunc}[4]{\{\msf{params}{:}~{#1};~\msf{locals}{:}~{#2};~\msf{return}~{#3};~\msf{body}{:}~{#4}\}} \newcommand{\wmodule}[1]{\{\msf{funcs}{:}~{#1}\}} \newcommand{\wcg}{\msf{globals}} \newcommand{\wcf}{\msf{funcs}} \newcommand{\wci}{\msf{instrs}} \newcommand{\wcs}{\msf{stack}} \newcommand{\wcl}{\msf{locals}} \newcommand{\wcm}{\msf{mem}} \newcommand{\wcmod}{\msf{module}} \newcommand{\wsteps}[2]{\steps{\brc{#1}}{\brc{#2}}} \newcommand{\with}{\underline{\msf{with}}} \newcommand{\wvalid}[2]{{#1} \vdash {#2}~\msf{valid}} % assign4.3 custom \newcommand{\wtry}[2]{\msf{try}~{#1}~\msf{catch}~{#2}} \newcommand{\wraise}{\msf{raise}} \newcommand{\wraising}[1]{\msf{raising}~{#1}} \newcommand{\wif}[2]{\msf{if}~{#1}~{\msf{else}}~{#2}} \newcommand{\wfor}[4]{\msf{for}~(\msf{init}~{#1})~(\msf{cond}~{#2})~(\msf{post}~{#3})~{#4}} \newcommand{\windirect}[1]{\msf{call\_indirect}~{#1}} % session types \newcommand{\ssend}[2]{\msf{send}~{#1};~{#2}} \newcommand{\srecv}[2]{\msf{recv}~{#1};~{#2}} \newcommand{\soffer}[4]{\msf{offer}~\{{#1}\colon({#2})\mid{#3}\colon({#4})\}} \newcommand{\schoose}[4]{\msf{choose}~\{{#1}\colon({#2})\mid{#3}\colon({#4})\}} \newcommand{\srec}[1]{\msf{label};~{#1}} \newcommand{\sgoto}[1]{\msf{goto}~{#1}} \newcommand{\dual}[1]{\overline{#1}} % Inference rules \newcommand{\inferrule}[3][]{\cfrac{#2}{#3}\;{#1}} \newcommand{\ir}[3]{\inferrule[\text{(#1)}]{#2}{#3}} \newcommand{\s}{\hspace{1em}} \newcommand{\nl}{\\[2em]} \newcommand{\evalto}{\boldsymbol{\overset{*}{\mapsto}}} \newcommand{\steps}[2]{#1 \boldsymbol{\mapsto} #2} \newcommand{\evals}[2]{#1 \evalto #2} \newcommand{\subst}[3]{[#1 \rightarrow #2] ~ #3} \newcommand{\dynJ}[2]{#1 \proves #2} \newcommand{\dynJC}[1]{\dynJ{\ctx}{#1}} \newcommand{\typeJ}[3]{#1 \proves \hasType{#2}{#3}} \newcommand{\typeJC}[2]{\typeJ{\ctx}{#1}{#2}} \newcommand{\hasType}[2]{#1 : #2} \newcommand{\val}[1]{#1~\msf{val}} \newcommand{\num}[1]{\msf{Int}(#1)} \newcommand{\err}[1]{#1~\msf{err}} \newcommand{\trans}[2]{#1 \leadsto #2} \newcommand{\size}[1]{\left|#1\right|} $$

&Notepad

Minimum effort investing

Will Crichton   —   April 15, 2016
If you don't have any investments, i.e. your money is sitting in a savings account, then you're missing out. Investing today is surprisingly easy with the advent of index funds, and I'll take you step by step through both the theory and the practical parts of settings up these investments for yourself. After reading this note and taking 30 minutes out of your day, you can be making 7-12% returns on your money with minimum effort.

Preface: None of this is legal financial advice and should be taken with a grain of salt. I’m a CS major, not a financial advisor.

Introduction to investing

Investing, or trading money for securities in the hope that they’ll gain value, is key to a sound financial future. The average interest rate, or percentage paid to you of your current balance, for savings accounts in banks is 0.06% 1, whereas investments can make double-digit returns year-over-year. Wisely investing your money helps finance your retirement and accumulate capital in the short term. However, prior to the last decade, intelligently investing required a finance degree and a Wall Street job due to the difficulty of picking individual stocks to buy or sell, known as day trading.

The trouble with day trading and picking stocks is that any given stock can have high variance, and putting all your eggs in one basket is a bad idea, particularly in the stock market. Moreover, the individual Joe Investor has zero chance at competing with enormous institutional funds or trading firms. The natural response, then, is to diversify. This gave rise to mutual funds, or pools of money managed by professional investors that are required by law to possess diverse securities. These fund managers require a fee, however, to decide what securities a mutual fund should invest in.

It turns out that there are some really simple mutual funds that get surprisingly good returns. For example, if you have a fund that just invests in every stock in the S&P 500, a popular listing of US companies, it can find returns close to or better than funds actively managed by professional investors. This gives rise to two phenomena: passive fund management, where diverse funds are created and don’t need constant rearrangement, and index funds.

Index funds

An index is something that tracks the value of a particular basket of stocks, usually listings like the S&P 500. Index funds are mutual funds whose components reflect a particular index. These funds have far lower commission fees because they are passively managed. This is what makes investing today so easy for the average Joe Investor: you can dump your money into an index fund and just let it grow.

To provide some concrete numbers: these index funds average anywhere from 5% to 12% average yearly returns on investment 2. That’s leagues better than letting your money languish in a savings account getting 0.06% interest. If you don’t have any investments, I implore you to set up them as soon as possible, because you’re missing out on a lot of potential profit. You might wonder, though, what’s the catch. Nobody gets free money. This is true–these index funds roughly track the health of the economy, so you will lose a good portion of your short-term funds if the economy takes a dive. Index fund investing is a statement that you believe the overall value of the economy will increase (which it historically has).

Setting up your investments

My general approach to financial management is this:

  1. Keep enough money in your spending account to handle day-to-day expenses. No more than $1000 (for me, at least).
  2. Keep at least six months of emergency savings in a savings account or in conservative investments (e.g. bonds).
  3. Invest as much as you can into your retirement account, this is probably $5,500 per year.
  4. Put the rest into index funds.

Hopefully you already have a bank account and can handle the first two steps. I’ll show you how to do the latter two steps in under 30 minutes. Many services offer index funds that you can invest in. I personally choose to use Vanguard since they’re trustworthy in the finance community for being consumer-driven and not profit-driven. They also have some of the lowest commission fees on the market for their funds.

You’re going to open two accounts: a Roth IRA (retirement account) and a Brokerage Account (for everything else). You can start by going through the Vanguard registration process and opening the Roth IRA.

Aside on IRAs: an IRA is a kind of account that’s intended for retirement savings. It has limits on the amount of money you can put in each year. The Roth IRA is cool because you don’t have to pay capital gains tax on the money you earn from its investments (this is a super good deal!). However, you can’t contribute to a Roth if you make over ~$110k.

Once you have the two accounts set up, do the following:

  1. Figure out how much money you’re going to set aside for your spending/savings accounts. Take the rest as investment funds.
  2. Put $5,500 into the Roth IRA. If you have less than that, put as much as you can and call it a day.
  3. I recommend investing all of it in the Vanguard Target Retirement 2060 Fund (note: you can buy funds by clicking on the Roth IRA account link and then clicking “Buy and Sell” > “Buy Vanguard Funds”). This particular fund is cool because they shift the underlying assets over time based on how close you are to retirement, but it’s still a low management fee.
  4. Put the rest of your investment funds into your brokerage account.
  5. Here it gets a bit more hazy. I encourage you to look at what mutual funds Vanguard offers and pick one that’s good for you—try out their fund recommender. Generally, your strategy should be to split your investments between stock indexes (risky securities) and bond indexes (stable securities). Start out with more stock holdings, and then as you get older, shift more of your money into bonds. According to Bogleheads, a good rule of thumb is to have “roughly your age in bonds,” so in your 20s you want 20ish percent bonds and 80 percent stocks. Specifically, I use a balance of the Vanguard Total Stock Market Index Fund and the Vanguard Total Bond Market Index Fund.

And that’s it! Your finances look a lot better than when your money was just sitting in a bank. Again, I want to reiterate that this is what I’ve learned over the last year from talking to friends and also interning at Jane Street. If you know a finance guru, great, ask them for advice. If, however, you’re like I was a year ago with no clue how to manage finances because no one ever told you, hopefully this post can put you on the right track.

If you have comments, questions, or critiques, feel free to contact me at crichton.will@gmail.com.

References

  1. http://www.gobankingrates.com/savings-account/what-average-savings-account-interest-rate/ 

  2. https://investor.vanguard.com/mutual-funds/list?assetclass=stk#/mutual-funds/asset-class/month-end-returns