Dynamic Valuation of Memory Semiconductor Stocks

Recently (July 2026), financial markets have exhibited behavior that appears irrational over short time horizons. In particular, memory semiconductor stocks have experienced unusually large price fluctuations despite exceptionally strong earnings. Leading companies such as Samsung Electronics, SK hynix, and Micron have traded at only 5--7 times forward P/E, a low valuation given their record profitability. 

The apparent contradiction reflects uncertainty about the appropriate valuation multiple. The market is caught between two opposing forces: robust earnings growth driven by AI infrastructure investment and the possibility that aggressive capital expenditures may eventually create excess capacity, leading to oversupply and weaker future profitability. Consequently, the key investment question is no longer, "How large are today's earnings?" Instead, the market asks, "Can today's earnings be sustained over many years?" Equivalently, investors focus less on the current level of earnings than on their dynamics. Rather than asking how large earnings are today, they ask whether earnings growth is accelerating or beginning to decelerate. Although global AI infrastructure is expected to continue expanding across North America, Europe, Asia, and other regions, uncertainty remains regarding the long-term balance between AI-driven demand and future supply. As a result, today's valuations reflect not only strong current fundamentals but also the market's expectations about the durability of future earnings.

The purpose of this blog is to present a brief mathematical perspective on the mechanisms underlying the recent behavior of memory semiconductor stocks. I am not an expert in financial markets; rather, I am a learner who enjoys applying mathematical tools to understand complex real-world phenomena. This blog was developed with the assistance of ChatGPT.

The 12-month forward price-to-earnings ratio (12M forward P/E) is defined by $\frac{P}{E_{12m}}$, where $P$ is the current stock price and $E_{12m}$ is the consensus estimate of earnings over the next twelve months. Many investors implicitly assume that a low forward P/E indicates undervaluation. However, the market does not price today's earnings alone. Instead, it prices the entire expected trajectory of future earnings. More generally, the stock price may be regarded as a function $P=f(E(t),R(t),S(t),\sigma(t)),$ where $E(t)$ denotes the expected earnings path, $R(t)$ the discount rate, $S(t)$ market supply--demand dynamics, and $\sigma(t)$ the uncertainty associated with future earnings and the macroeconomic environment. From this perspective, valuation is only one component of a multidimensional dynamic system.

The first derivative, $\frac{dE}{dt}$, represents the earnings growth rate, whereas the second derivative, $\frac{d^2E}{dt^2}$, measures the acceleration or deceleration of earnings growth. In the second quarter of 2026, leading memory semiconductor companies such as Micron, SK hynix, and Samsung Electronics reported record earnings and historically high profitability. Nevertheless, the market appeared to assume that $\frac{d^2E}{dt^2}\lesssim0$, implying that earnings growth was approaching its peak or beginning to decelerate even though the absolute level of earnings remained exceptionally high. Consequently, valuation multiples contracted despite outstanding current profitability.

From a mathematical perspective, the market discounts not only the expected earnings path $E(t)$, but also its derivatives. In other words, valuation depends on the level, the slope, and the curvature of the expected earnings trajectory. This interpretation also explains why investment firms publish remarkably different target prices.

For simplicity, suppose every institution agrees on the same forecast of 12-month forward earnings per share, denoted by $E^{f}$. Then the target price estimated by institution $i$ is $P_i^{*}=E^{f}M_i$, where $M_i$ denotes the forward valuation multiple assigned by institution $i$. The valuation multiple itself can be viewed as a function $M_i=g(R_i,S_i,\sigma_i)$, where $R_i$ denotes the discount rate, $S_i$ summarizes the institution's assumptions regarding the long-term supply--demand balance, and $\sigma_i$ represents its assessment of uncertainty. Consequently, $P_i^{*}=E^{f}g(R_i,S_i,\sigma_i)$.

Analysts who believe that AI-driven memory demand will remain strong for many years assign a larger valuation multiple and therefore obtain a higher target price. In contrast, analysts who believe that the current earnings cycle is approaching its peak assign a smaller valuation multiple, anticipating that future oversupply and slower earnings growth will eventually reduce profitability.Thus, even if different institutions have nearly identical earnings forecasts, modest differences in their assumptions regarding future demand, oversupply risk, discount rates, competitive conditions, and uncertainty can produce substantially different target prices.

Of course, valuation alone does not determine market prices. Short-term prices are also influenced by market microstructure. A simple representation is $P(t)=V(t)+N(t)$, where $V(t)$ denotes the intrinsic value implied by long-term fundamentals and $N(t)$ represents temporary deviations caused by liquidity constraints, investor sentiment, systematic trading, and other non-fundamental effects.

During periods of market stress, the magnitude of $N(t)$ may temporarily exceed changes in intrinsic value, causing prices to deviate substantially from their fundamental values. One important source of market microstructure is leveraged ETF rebalancing.

Let $X_t$ denote the target exposure at time $t$, $L$ the leverage ratio ($L=2$ for a 2$\times$ ETF), and $A_t$ the ETF's net asset value. The target exposure is $X_t=LA_t.$ If the underlying stock moves by a daily return $r$, the ETF must rebalance its position approximately by $\Delta X\approx L A_t r,$ where $\Delta X$ is the amount of exposure that must be bought ($\Delta X>0$) or sold ($\Delta X<0$) in order to maintain the target leverage.

For a 2$\times$ leveraged ETF, $\Delta X\approx 2A_t r.$ If the stock price falls by $a\times 100\%$, then $r=-a$, and therefore $\Delta X\approx -2A_ta.$ Hence, to maintain a leverage ratio of $L=2$, the ETF must sell approximately $2a\times A_t$ worth of the exposure.Thus, a 2$\times$ leveraged ETF is structurally forced to buy when the underlying stock rises ( $r>0 \rightarrow \Delta X>0$),  and sell when it falls ($r<0  \rightarrow \Delta X<0$).  This procyclical trading mechanism reinforces existing price movements. When leveraged ETFs become sufficiently large relative to the underlying stock's trading activity, their end-of-day rebalancing can amplify short-term volatility. Similar feedback mechanisms also arise from margin calls, forced liquidations, and algorithmic trading.

An additional consequence of daily leverage resetting is volatility decay, also known as negative compounding. Unlike a static $2\times$ investment, a leveraged ETF delivers approximately twice the daily return, so its cumulative return over multiple trading days is $R_L=\prod_{t=1}^{n}(1+Lr_t)-1$, which generally differs from $L(\prod_{t=1}^{n}(1+r_t)-1)$. For example, if the underlying stock rises by $10\%$ on one day and falls by $10\%$ on the next, the cumulative return of the underlying stock is $1.1\times0.9=0.99$, corresponding to a loss of only $1\%$. In contrast, a $2\times$ leveraged ETF evolves as$1.2\times0.8=0.96,$ corresponding to a loss of $4\%$.  More generally, if returns alternate between $+r$ and $-r$, the underlying stock evolves as $(1+r)(1-r)=1-r^2$, whereas the leveraged ETF evolves as $(1+Lr)(1-Lr)=1-L^2r^2$. Hence, the cumulative loss generated purely by volatility scales approximately with the square of the leverage ratio, $L^2$. Consequently, repeated large daily fluctuations can substantially erode the value of leveraged ETFs even when the underlying stock experiences only a modest net price change. This erosion often induces additional investor selling, redemptions, and position reductions, generating further rebalancing trades and strengthening the feedback effects described above.

In South Korea, this issue is particularly important because Samsung Electronics and SK Hynix together account for more than half of the KOSPI's market capitalization, making price fluctuations in these two stocks capable of affecting the entire market. Moreover, trading in single-stock leveraged ETFs on these companies has become unusually active relative to the underlying stocks, increasing the market's sensitivity to predictable rebalancing flows. 

However, the 7–8$\%$ daily swings in Samsung Electronics and SK Hynix during July 1–10, 2026 cannot be explained by leveraged ETF rebalancing alone, since the ETFs' direct rebalancing trades remain small relative to the stocks' total daily turnover. A more plausible explanation is a positive feedback mechanism. Because leveraged ETFs rebalance near the market close, these trades are highly predictable. Quantitative funds, high-frequency traders, arbitrageurs, and momentum traders often anticipate the expected ETF demand or supply and trade ahead of it, reinforcing the initial price movement. The same mechanism operates in reverse during market declines. Consequently, the observed volatility is likely driven not by ETF rebalancing itself, but by the interaction between predictable ETF rebalancing, anticipatory trading, and other feedback mechanisms, creating a self-reinforcing positive feedback loop.