Life with Physics

U.S. Treasury notes or bonds pay a coupon every six month and return the face value at maturity. The price of a $N$-year Treasury bond equals to the present value of all future cash flows: \begin{equation}P=\frac{\frac{r}{2} * F}{1+ \frac{y}{2}} + \frac{\frac{r}{2} * F}{(1+ \frac{y}{2})^2} +\cdots + \frac{\frac{r}{2} * F}{(1+ \frac{y}{2})^{2N}} + \frac{ F}{(1+ \frac{y}{2})^{2N}}\,,\tag{1}\end{equation} which can be simplified as \begin{equation}\frac{P}{F}= \frac{r}{y}+\frac{1-\frac{r}{y}}{(1+ \frac{y}{2})^{2N}}\,.\tag{2}\end{equation} where $P$ is the bond price and $F$ is the face value of the bond. $r$ is the coupon rate (or the interest rate in Treasury documents) and $y$ is the yield to maturity. Eq. (1) and (2) are computed in a semi-annual basis: there are $2N$ periods for a $N$-year bond. For the recent 30-Year Treasury bond, the issue date is Aug. 15, 2024 and the maturity date is Aug. 15, 2054. Submitting the coupon rate $r=4.250\%$ and the yield to maturity $y=4.314\%$ into ...

This post is for knowledge sharing only. It is not intended to be investment or tax advice. BOXX ETF  is a new financial product that offers nearly identical returns and risks to treasury bills, yet it may be more tax-efficient:  You only have to pay capital gain tax on the shares you sell, not on all the savings you have. If you hold onto the shares you sell for over a year, you'll pay the long-term capital gains tax, which is lower than the tax on both ordinary interest and treasury interest. Sell shares within a year of buying them, and you'll pay short-term capital gains tax. It's the same rate as the tax rate of ordinary income but higher than the tax rate of treasury interest. Heavy tax on interest Every family should maintain some cash reserve as family emergency fund. The headache is that the interest generated from such cash reserve is taxed as ordinary income each year. For high income earners in California, The tax rate on interest can be as high as 51% includin...

This post is for knowledge sharing only. It is not intended to be tax or investment advice. 1. Contribute to pre-tax 401K and HSA As well known, pre-tax 401K and health saving account (HSA) are the only a few tax shelters for W2 workers.  2. Tax-loss harvesting If your total capital losses exceed your capital gains in a tax year, you can deduct up to \$3,000 (married filing jointly) from your ordinary income. If your losses are more than $3,000, you can carry over the remaining amount to future years, continuing to offset your income until all the losses are used up. A popular method to generate these deductible losses is  tax-loss harvesting . This involves selling a security at a loss to offset gains or reduce ordinary income, and optionally purchasing a similar, but not "substantially identical", security to avoid missing out on the market. However, be aware of the  wash-sale rule , which disallows claiming a loss if you buy the same or a substantially identical...

This post is for knowledge sharing only. It is not intended to be tax or legal advice. I used to believe that trusts were only for the wealthy. But recently, I learned that there is at least one trust that ordinary families, especially those living in California, should establish for seamless family wealth inheritance: a revocable living trust. One may need to find a lawyer on the estate planning to discuss and set up a revocable living trust. But it is still good to learn some background knowledge before talking to a lawyer.   Why revocable living trust A revocable living trust, as implied by its name, allows the grantor (who created the trust) to make changes or completely revoke the trust while they are still alive. This means the grantor maintains full control over the assets placed within the trust. As a result, assets held in a revocable living trust are NOT protected from creditors. Avoid Probate The primary reason to establish a revocable living trust is to avoid prob...

 This post is for knowledge sharing only. It is not intended to be investment or tax advice. Highlight There are a lot of ETF s on the market. Personally, I only prefer the following two ETFs for long term investments: VOO  (or IVV ): Both VOO and IVV passively track the well known S&P 500 index . The expense ratios of VOO and IVV are the same: 0.03%. SPY also tracks S&P 500 index but with a higher expense ratio: 0.0945%. It is more suitable for trading rather than buying and holding. QQQM (or QQQ ): Both QQQM and QQQ passively track the Nasdaq 100 index . They are almost identical. QQQM is a newer ETF launched very recently for buying and holding. The expense ratio of QQQM is 0.15% while the expense ratio QQQ is 0.2%. Notes on QQQM (or QQQ): Although QQQM concentrates heavily on tech companies, fundamentally it is NOT a  sector ETF . For example, in the top 10 holdings of QQQM as of January 2024, we see the name of Costco Wholesale that belongs to the cons...

This post is for knowledge sharing only. It is not intended to be investment or tax advice. If one does not manually select or change investments,  the default investment options in most 401K plans are usually some target data funds similar to  Vanguard Target Retirement Funds . Such funds are dynamically mixed with stocks and bonds, and the asset allocation gradually weights more to bonds from stocks. My personal opinion is very simple: NO target date funds.  Instead, choose a low-cost S&P 500 index fund in the 401K plan. Here are the main reasons: The fees of target date funds are high. For example, the expense ratio of  Vanguard Target Retirement Funds  is 0.08%. Some target funds are even more expensive. In contrast, the expense ratio of  Vanguard 500 Index Fund Institutional Select Shares is only 0.01%. The long term performance is worse than the S&P 500 index. This is not surprising because of the existence of bonds in the target date funds. ...

This post is for knowledge sharing only. It is not intended to be investment or tax advice. 529 Plans are tax-advantaged accounts specific for education saving: Contribution are made with after-tax dollars. Growth within the account is tax-free. Withdraw for qualified education expenses is also tax free. Roth IRA First 529 Plans are very similar to Roth IRA . But Roth IRA withdraw under  the 5-year rule  is tax free for any purpose. Therefore, unless for the state tax deduction in some states, it is always better to max out Roth IRA first (through backdoor and mega backdoor  for high income earners) before funding a 529 plan. Note: there is NO California state tax deduction for any 529 plan. 529 or Not? Here are some considerations in reality before funding a 529 plan: What if no qualified education expenses In the worst case that there will be no qualified education expenses, you can still take money out for non-qualified expenses, but you have to pay: federal income ta...

This post is for knowledge sharing only. It is not intended to be investment or tax advice. [Update] Consider BOXX ETF for more tax advantages. Before investing risky assets, one should reserve enough cash for both expected expenses (like down payment of home purchase) and unexpected expenses (in case of layoff for example).  The goal of cash reserve is NOT high return, but safety and liquidity . Even so, we still want to earn some interest from the cash reserve. In the table below, we list some common options for high income CA residents to park cash reserve for a relatively high interest rate or after tax earnings as of  January 12, 2024 . Note that interest is taxed as ordinary income plus a so called  net investment income tax . The total tax rate can be as high as 51% including 37% federal income tax, around 10% CA state income tax and nearly 4% net investment income tax. Account Interest Rate Total Tax Rate After Tax Earning Marcus High Yield Savi...

This post is for knowledge sharing only. It is not intended to be investment or tax advice. In U.S. the tax rate on the capital earnings in 2024 can be as high as 20% + 10% + 4% = 34% for long term capital gains and qualified dividends . 37% + 10% + 4% = 51% for short term capital gain , ordinary dividends and interests  (all taxed as ordinary income). Notes: 20% is the highest federal tax bracket of long term capital gain while 37% is the highest federal income tax bracket.  10% is the CA state income tax. CA tax treats all capital gains as ordinary income, without distinction between short term and long term. 4% is the so-called net investment income tax for high income earners, which is less known. For high income earners, it is really not a good idea to do short-term trading from the tax perspective. Even for long-term trading, one third of the earnings will be paid as taxes. Instead, the buy and hold strategy may be preferred. Note that there is NO tax on the asse...

This post is for knowledge sharing only. It is not intended to be investment or tax advice. Health saving account (HSA) is another tax-free investment account that is even better than Roth IRA . HSA offers three tax advantages: The contribution is tax deductible. Investment grows tax-free. Finally, withdrawals for qualified medical expenses are also tax-free. To fully utilizes the advantages, it is better to let the money stay and grow in HSA as long as possible. To achieve this, Do NOT use HSA money to cover the current medical expenses. Instead, save the receipts and ask for reimbursement in future year of withdrawal. Remarks: HSA does NOT have any CA state tax benefits. Both HSA enrollees and their spouse are NOT eligible to contribute to the general   flexible spending account (FSA) . One can have a HSA and  limited purpose FSA (LPFSA) at the same time. Unlike the general FSA, LPFSA can only cover vision and dental expenses. High Deduction v.s. HSA Saving To be eligible ...

This post is for knowledge sharing only. It is not intended to be investment or tax advice. 0. Account Overview  Table 1 Common retirement  accounts in U.S. I summarizes the common retirement accounts in Table 1:  The second row in Table 1 lists the company-sponsored accounts that are offered through employers. The third row in Table 1 lists the individual retirement accounts (IRA) that is unrelated to employments. The columns in Table 1 are about different tax advantages as described below. WARNING: because of the tax advantages, there are also limitations and specific rules imposed by IRS for early withdrawal before the retirement age. For accounts listed in the second column,  Contributions are made with before-tax dollars . The money taken out will be taxed as regular income in the year of withdrawal. For accounts listed in the third column,  Contributions are made with after-tax dollars . The money taken out is  tax free . For after-tax 401K in the fou...

 The formula of the monthly mortgage payments for a fixed-rate loan can be found online as \begin{equation} M = P\frac{r(1+r)^n}{(1+r)^n-1}\,,\tag{1}\end{equation} where  $M$ is the mortgage payment.   $P$ is the principal, i.e., the initial amount borrowed.  $r$ is the monthly interest rate. For annual interest rate $2.5\%$, $r=2.5\% / 12$. $n$ is the number of payments. For 30-years fixed rate mortgage, $n=30 * 12 = 360$. Here we provide a derivation of the above formula. Let $b_i$ be the owned balance in the $i$-th month. Initially, $b_0=P$ and we choose the constant monthly payment $M$ such that $b_n=0$. We then have the recursion relation between two consecutive month as \begin{equation}b_{i+1}=b_i(1+r) - M\,.\tag{2}\end{equation} A trick to solve (2) is to write Eq. (2) into the following form \begin{equation}b_{i+1}+C = \left(b_i+C\right)(1+r)\,,\tag{3}\end{equation} so that $b_i+C$ is a geometric sequence: \begin{equation}b_i + C = (b_0 + C) (1+r)^i\,.\end{eq...